Method and apparatus for photomask image registration

• US 7,260,813 B2
• Filed: 10/25/2004
• Issued: 08/21/2007
• Est. Priority Date: 10/25/2004
• Status: Active Grant

• Current Assignee: Synopsys Incorporated
• Original Assignee: Synopsys Incorporated
• Inventors: Nogatch, John T., Du, Robert W., Lesnick, Ronald J. Jr.
• Primary Examiner(s): Lin; Sun James
• Application Number:
  US10/973,890
• Publication Number:
  US 20060088200A1
• Time in Patent Office: 1,030 Days
• Field of Search: 716/21, 716/19, 716/4
• US Class Current: 716/51
• CPC Class Codes: G03F 1/84 Inspecting
• CPC Class Codes: G06T 2207/30148 Semiconductor; IC; Wafer
• CPC Class Codes: G06T 7/001 using an image reference approach
• CPC Class Codes: G06T 7/32 using correlation-based methods

Abstract

One embodiment of the present invention provides a system that computes translational differentials between a database-image and a scanned-image of a photomask. During operation, the system receives a noise-free database-image and a scanned-image that is generated by an imaging process. Next, the system determines whether the database-image has complex geometry and whether the database-image is a line-and-space pattern. If the database-image is a line-and-space pattern, the system first converts the scanned-image into a polarity-enhanced-image. The system then computes translational differentials by performing a correlation using the database-image and the polarity-enhanced-image. On the other hand, if the database-image is not a line-and-space pattern, the system computes translational differentials by performing a correlation using the database-image and the scanned-image. Note that the accuracy of the computed translational differentials is significantly increased because the system chooses a technique for computing the translational differentials which is suitable for the type of pattern present in the database-image.

Claims

1. A method for computing translational differentials between a database-image and a scanned-image of a photomask, the method comprising:

receiving the database-image that is noise free and the scanned-image that is generated by an imaging process;

determining whether the database-image is a line-and-space pattern;

if the database-image is a line-and-space pattern,

converting the scanned-image into a polarity-enhanced-image; and

computing translational differentials by performing a correlation using the database-image and the polarity-enhanced-image;

otherwise, if the database-image is not a line-and-space pattern, computing translational differentials by performing a correlation using the database-image and the scanned-image;

wherein accuracy of the computed translational differentials is significantly increased because the method chooses a technique for computing the translational differentials which is suitable for a type of pattern present in the database-image.

2. The method of claim 1, wherein the determining whether the database-image is a line-and-space pattern involves:

computing database-projection-vectors using the database-image by taking orthogonal projections along a set of directions; and

determining whether only one of the computed database-projection-vectors contains a square-wave pattern, while other computed database-projection vectors contain a straight line.

3. The method of claim 1, wherein the converting the scanned-image into a polarity-enhanced-image involves:

identifying a projection-direction for which a corresponding database-projection-vector contains a square-wave pattern, wherein the corresponding database-projection-vector is computed using the database-image by taking an orthogonal projection along the projection-direction;

computing a scanned-projection-vector using the scanned-image by taking an orthogonal projection along the projection-direction;

identifying peaks in the computed scanned-projection-vector;

categorizing an inter-peak interval by comparing values at the edges of the inter-peak interval with an average value over the inter-peak interval; and

changing a value of a pixel in the scanned-image based on the category of a corresponding inter-peak interval, wherein a pixel corresponds to an inter-peak interval if, while taking an orthogonal projection along the projection-direction, the pixel contributes to an element in the inter-peak interval.

4. The method of claim 1, wherein the computing translational differentials by performing a correlation using the database-image and the scanned-image involves:

determining whether the database-image has a complex geometry;

if the database-image has a complex geometry, computing translational differentials using a correlation-filter based approach;

otherwise, if the database image does not have a complex geometry, computing translational differentials using an orthogonal-projection based approach.

5. The method of claim 4, wherein the determining whether the database-image has a complex geometry involves:

computing database-projection-vectors using the database-image by taking orthogonal projections along a set of directions;

differentiating the database-projection-vectors to obtain differentiated database-projection-vectors; and

determining whether one or more of said differentiated database-projection-vectors contain many non-zero elements.

6. The method of claim 4, wherein the computing translational differentials using a correlation-filter based approach involves:

tiling the scanned image and the database image to obtain a tiled scanned-image and a tiled database-image, respectively, wherein the tiled scanned-image contains a set of sub-images which are decimated versions of the scanned image and the tiled database-image contains a set of sub-images which are decimated versions of the database image;

converting the tiled scanned-image and the tiled database-image into a windowed scanned-image and a windowed database-image, respectively, by windowing each sub-image in the tiled scanned-image and the tiled database-image;

applying a fast-Fourier-transform to the windowed scanned-image to obtain a transformed-image;

applying a correlation-filter-template to the transformed-image to obtain a filtered-image;

performing an inverse-fast-Fourier-transform using the filtered-image and a fast-Fourier-transform of the windowed database-image to obtain a correlation-function;

identifying a peak in the correlation-function; and

computing the translational differentials based on location of the identified peak.

7. The method of claim 4, wherein the computing translational differentials using an orthogonal-projection based approach involves:

computing a set of candidate-translational-differentials using the database-image and the scanned-image;

generating one or more sets of translated directional-gradient-images based on the set of candidate-translational-differentials and using the database-image and the scanned-image;

converting the database-image into a set of smoothed directional-gradient-images; and

computing the translational differentials by performing a normalized correlation using the set of smoothed directional-gradient-images and the one or more sets of translated directional-gradient-images;

wherein computational time is significantly reduced because the method performs normalized correlation using the set of candidate-translational-differentials, instead of exhaustively performing normalized correlation using all possible translational differentials.

8. The method of claim 7, wherein the computing a set of candidate-translational-differentials using the database-image and the scanned-image involves:

converting the database-image and the scanned-image into a database-gradient-image and a scanned-gradient-image, respectively;

computing database-projection-vectors from the database-gradient-image and scanned-projection-vectors from the scanned-gradient-image by taking orthogonal projections along a set of directions;

extracting correlation-vectors from the computed database-projection-vectors;

mapping the scanned-projection-vectors to obtain accumulator-vectors in an accumulator space by using the correlation-vectors; and

computing a set of candidate-translational-differentials based on peak-cluster locations in the accumulator space, wherein a peak-cluster is a collection of contiguous elements around a peak (including the peak).

9. The method of claim 8, wherein the converting the database-image and the scanned-image into a database-gradient-image and a scanned-gradient-image involves:

creating a directional-gradient filter using the database-image, wherein the directional-gradient filter can be used to attenuate edgels that do not conform to directional gradients of feature edges in the database-image;

converting the database-image and the scanned-image into a set of database directional-gradient-images and a set of scanned directional-gradient-images, respectively;

generating a raw database-gradient-image and a raw scanned-gradient-image from the set of database directional-gradient-images and the set of scanned directional-gradient-images, respectively; and

applying the directional-gradient filter to the raw database-gradient-image and the raw scanned-gradient-image to obtain the database-gradient-image and the scanned-gradient-image, respectively.

10. The method of claim 8, wherein the generating one or more sets of translated directional-gradient-images based on the set of candidate-translational-differentials involves:

de-projecting only cluster-peaks in the accumulator-vectors to obtain reconstructed scanned-projection-vectors;

de-projecting the reconstructed scanned-projection-vectors to obtain reconstructed directional-gradient-images; and

generating one or more sets of translated directional-gradient-images by displacing the reconstructed directional-gradient-images using the set of candidate-translational-differentials;

wherein de-projecting only the cluster-peaks improves signal-to-noise ratio of the reconstructed directional-gradient-images.

11. The method of claim 9, wherein the creating a directional-gradient filter involves:

convolving the database-image with a horizontal and a vertical Point Spread Function (PSF) to generate a horizontal edgel-image and a vertical edgel-image, respectively;

computing a gradient-magnitude-image using the horizontal edgel-image and the vertical edgel-image;

applying a clip-low filter to the gradient-magnitude-image to obtain a clipped-gradient-image;

generating a histogram using gradient orientations in the clipped-gradient-image; and

creating the directional-gradient filter using the histogram.

12. The method of claim 7, wherein the converting the database-image into a set of smoothed directional-gradient-images involves:

converting the database-gradient-image into a set of unsmoothed directional-gradient-images; and

applying a low-pass filter to the set of unsmoothed directional-gradient-images to obtain the set of smoothed directional-gradient-images.

13. A method for computing translational differentials between a database-image and a scanned-image of a photomask, the method comprising:

receiving the database-image that is noise free and the scanned-image that is generated by an imaging process;

determining whether the database-image has a complex geometry;

determining whether the database-image is a line-and-space pattern;

if the database-image is a line-and-space pattern,

converting the scanned-image into a polarity-enhanced-image; and

computing translational differentials by performing a correlation using the database-image and the polarity-enhanced-image;

otherwise, if the database-image is not a line-and-space pattern, but has a complex geometry, computing translational differentials using a correlation-filter based approach using the database-image and the scanned-image;

otherwise, if the database-image is not a line-and-space pattern and does not have a complex geometry, computing translational differentials using an orthogonal-projection based approach using the database-image and the scanned-image;

wherein accuracy of the computed translational differentials is significantly increased because the method chooses a technique for computing the translational differentials which is suitable for a type of pattern present in the database-image.

14. A computer-readable storage medium storing instructions that, when executed by a computer, cause the computer to perform a method for computing translational differentials between a database-image and a scanned-image of a photomask, the method comprising:

receiving the database-image that is noise free and the scanned-image that is generated by an imaging process;

determining whether the database-image is a line-and-space pattern;

if the database-image is a line-and-space pattern,

converting the scanned-image into a polarity-enhanced-image; and

computing translational differentials by performing a correlation using the database-image and the polarity-enhanced-image;

otherwise, if the database-image is not a line-and-space pattern, computing translational differentials by performing a correlation using the database-image and the scanned-image;

wherein accuracy of the computed translational differentials is significantly increased because the method chooses a technique for computing the translational differentials which is suitable for a type of pattern present in the database-image.

15. The computer-readable storage medium of claim 14, wherein the determining whether the database-image is a line-and-space pattern involves:

computing database-projection-vectors using the database-image by taking orthogonal projections along a set of directions; and

determining whether only one of the computed database-projection-vectors contains a square-wave pattern, while other computed database-projection vectors contain a straight line.

16. The computer-readable storage medium of claim 14, wherein the converting the scanned-image into a polarity-enhanced-image involves:

identifying a projection-direction for which a corresponding database-projection-vector contains a square-wave pattern, wherein the corresponding database-projection-vector is computed using the database-image by taking an orthogonal projection along the projection-direction;

computing a scanned-projection-vector using the scanned-image by taking an orthogonal projection along the projection-direction;

identifying peaks in the computed scanned-projection-vector;

categorizing an inter-peak interval by comparing values at the edges of the inter-peak interval with an average value over the inter-peak interval; and

changing a value of a pixel in the scanned-image based on the category of a corresponding inter-peak interval, wherein a pixel corresponds to an inter-peak interval if, while taking an orthogonal projection along the projection-direction, the pixel contributes to an element in the inter-peak interval.

17. The computer-readable storage medium of claim 14, wherein the computing translational differentials by performing a correlation using the database-image and the scanned-image involves:

determining whether the database-image has a complex geometry;

if the database-image has a complex geometry, computing translational differentials using a correlation-filter based approach;

otherwise, if the database image does not have a complex geometry, computing translational differentials using an orthogonal-projection based approach.

18. The computer-readable storage medium of claim 17, wherein the determining whether the database-image has a complex geometry involves:

computing database-projection-vectors using the database-image by taking orthogonal projections along a set of directions;

differentiating the database-projection-vectors to obtain differentiated database-projection-vectors; and

determining whether one or more of said differentiated database-projection-vectors contain many non-zero elements.

19. The computer-readable storage medium of claim 17, wherein the computing translational differentials using a correlation-filter based approach involves:

tiling the scanned image and the database image to obtain a tiled scanned-image and a tiled database-image, respectively, wherein the tiled scanned-image contains a set of sub-images which are decimated versions of the scanned image and the tiled database-image contains a set of sub-images which are decimated versions of the database image;

converting the tiled scanned-image and the tiled database-image into a windowed scanned-image and a windowed database-image, respectively, by windowing each sub-image in the tiled scanned-image and the tiled database-image;

applying a fast-Fourier-transform to the windowed scanned-image to obtain a transformed-image;

applying a correlation-filter-template to the transformed-image to obtain a filtered-image;

performing an inverse-fast-Fourier-transform using the filtered-image and a fast-Fourier-transform of the windowed database-image to obtain a correlation-function;

identifying a peak in the correlation-function; and

computing the translational differentials based on location of the identified peak.

20. The computer-readable storage medium of claim 17, wherein the computing translational differentials using an orthogonal-projection based approach involves:

computing a set of candidate-translational-differentials using the database-image and the scanned-image;

generating one or more sets of translated directional-gradient-images based on the set of candidate-translational-differentials and using the database-image and the scanned-image;

converting the database-image into a set of smoothed directional-gradient-images; and

computing the translational differentials by performing a normalized correlation using the set of smoothed directional-gradient-images and the one or more sets of translated directional-gradient-images;

wherein computational time is significantly reduced because the method performs normalized correlation using the set of candidate-translational-differentials, instead of exhaustively performing normalized correlation using all possible translational differentials.

21. The computer-readable storage medium of claim 20, wherein the computing a set of candidate-translational-differentials using the database-image and the scanned-image involves:

converting the database-image and the scanned-image into a database-gradient-image and a scanned-gradient-image, respectively;

computing database-projection-vectors from the database-gradient-image and scanned-projection-vectors from the scanned-gradient-image by taking orthogonal projections along a set of directions;

extracting correlation-vectors from the computed database-projection-vectors;

mapping the scanned-projection-vectors to obtain accumulator-vectors in an accumulator space by using the correlation-vectors; and

computing a set of candidate-translational-differentials based on peak-cluster locations in the accumulator space, wherein a peak-cluster is a collection of contiguous elements around a peak (including the peak).

22. The computer-readable storage medium of claim 21, wherein the converting a database-image and a scanned-image into the database-gradient-image and the scanned-gradient-image involves:

creating a directional-gradient filter using the database-image, wherein the directional-gradient filter can be used to attenuate edgels that do not conform to directional gradients of feature edges in the database-image;

converting the database-image and the scanned-image into a set of database directional-gradient-images and a set of scanned directional-gradient-images, respectively;

generating a raw database-gradient-image and a raw scanned-gradient-image from the set of database directional-gradient-images and the set of scanned directional-gradient-images, respectively; and

applying the directional-gradient filter to the raw database-gradient-image and the raw scanned-gradient-image to obtain the database-gradient-image and the scanned-gradient-image, respectively.

23. The computer-readable storage medium of claim 21, wherein the generating one or more sets of translated directional-gradient-images based on the set of candidate-translational-differentials involves:

de-projecting only cluster-peaks in the accumulator-vectors to obtain reconstructed scanned-projection-vectors;

de-projecting the reconstructed scanned-projection-vectors to obtain reconstructed directional-gradient-images; and

generating one or more sets of translated directional-gradient-images by displacing the reconstructed directional-gradient-images using the set of candidate-translational-differentials;

wherein de-projecting only the cluster-peaks improves signal-to-noise ratio of the reconstructed directional-gradient-images.

24. The computer-readable storage medium of claim 22, wherein the creating a directional-gradient filter involves:

convolving the database-image with a horizontal and a vertical Point Spread Function (PSF) to generate a horizontal edgel-image and a vertical edgel-image, respectively;

computing a gradient-magnitude-image using the horizontal edgel-image and the vertical edgel-image;

applying a clip-low filter to the gradient-magnitude-image to obtain a clipped-gradient-image;

generating a histogram using the-gradient orientations in the clipped-gradient-image; and

creating the directional-gradient filter using the histogram.

25. The computer-readable storage medium of claim 20, wherein the converting the database-image into a set of smoothed directional-gradient-images involves:

converting the database-gradient-image into a set of unsmoothed directional-gradient-images; and

applying a low-pass filter to the set of unsmoothed directional-gradient-images to obtain the set of smoothed directional-gradient-images.

26. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for computing translational differentials between a database-image and a scanned-image of a photomask, the method comprising:

receiving the database-image that is noise free and the scanned-image that is generated by an imaging process;

determining whether the database-image has a complex geometry;

determining whether the database-image is a line-and-space pattern;

if the database-image is a line-and-space pattern,

converting the scanned-image into a polarity-enhanced-image; and

computing translational differentials by performing a correlation using the database-image and the polarity-enhanced-image;

otherwise, if the database-image is not a line-and-space pattern but has a complex geometry, computing translational differentials using a correlation-filter based approach using the database-image and the scanned-image;

otherwise, if the database-image is not a line-and-space pattern and does not have a complex geometry, computing translational differentials using an orthogonal-projection based approach using the database-image and the scanned-image;

wherein accuracy of the computed translational differentials is significantly increased because the method chooses a technique for computing the translational differentials which is suitable for a type of pattern present in the database-image.

27. An apparatus for computing translational differentials between a database-image and a scanned-image of a photomask, the apparatus comprising:

a receiving-mechanism configured to receive the database-image that is noise free and the scanned-image that is generated by an imaging process;

a pattern-determining mechanism configured to determine whether the database-image is a line-and-space pattern;

a computing mechanism, wherein if the database-image is a line-and-space pattern, the computing mechanism is configured to,

convert the scanned-image into a polarity-enhanced-image; and

compute translational differentials by performing a correlation using the database-image and the polarity-enhanced-image;

otherwise, if the database-image is not a line-and-space pattern, the computing mechanism is configured to compute translational differentials by performing a correlation using the database-image and the scanned-image;

wherein accuracy of the computed translational differentials is significantly increased because the apparatus chooses a technique for computing the translational differentials which is suitable for a type of pattern present in the database-image.

28. The apparatus of claim 27, wherein the pattern-determining mechanism includes:

a vector-computing mechanism configured to compute database-projection-vectors using the database-image by taking orthogonal projections along a set of directions; and

a second pattern-determining mechanism configured to determine whether only one of the computed database-projection-vectors contains a square-wave pattern, while other database-projection vectors contain a straight line.

29. The apparatus of claim 27, wherein the computing mechanism includes:

a direction-identifying mechanism configured to identify a projection-direction for which a corresponding database-projection-vector contains a square-wave pattern, wherein the corresponding database-projection-vector is computed using the database-image by taking an orthogonal projection along the projection-direction;

a vector-computing mechanism configured to compute a scanned-projection-vector using the scanned-image by taking an orthogonal projection along the projection-direction;

a peak-identifying mechanism configured to identify peaks in the computed scanned-projection-vector;

an interval-categorizing mechanism configured to categorized an inter-peak interval by comparing values at the edges of the inter-peak interval with an average value over the inter-peak interval; and

a pixel-changing mechanism configured to change a value of a pixel in the scanned-image based on the category of a corresponding inter-peak interval, wherein a pixel corresponds to an inter-peak interval if, while taking an orthogonal projection along the projection-direction, the pixel contributes to an element in the inter-peak interval.

30. The apparatus of claim 27, wherein the computing mechanism includes:

a geometry-determining mechanism configured to determine whether the database-image has a complex geometry;

a second computing mechanism, wherein if the database-image has a complex geometry, the second computing mechanism is configured to compute translational differentials using a correlation-filter based approach;

otherwise, if the database image does not have a complex geometry, the second computing mechanism is configured to compute translational differentials using an orthogonal-projection based approach.

31. The apparatus of claim 30, wherein the geometry-determining mechanism includes:

a vector-computing mechanism configured to compute database-projection-vectors using the database-image by taking orthogonal projections along a set of directions;

a differentiating mechanism configured to differentiate the database-projection-vectors to obtain differentiated database-projection-vectors; and

an element-counting mechanism configured to determine whether one or more of said differentiated database-projection-vectors contain many non-zero elements.

32. The apparatus of claim 30, wherein the second computing mechanism includes:

a tiling-mechanism configured to tile the scanned image and the database image to obtain a tiled scanned-image and a tiled database-image, respectively, wherein the tiled scanned-image contains a set of sub-images which are decimated versions of the scanned image and the tiled database-image contains a set of sub-images which are decimated versions of the database image;

an image-converting mechanism configured to convert the tiled scanned-image and the tiled database-image into a windowed scanned-image and a windowed database-image, respectively, by windowing each sub-image in the tiled scanned-image and the tiled database-image;

a transform-applying mechanism configured to apply a fast-Fourier-transform to the windowed scanned-image to obtain a transformed-image;

a filter-applying mechanism configured to apply a correlation-filter-template to the transformed image to obtain a filtered-image;

a transform-performing mechanism configured to perform an inverse-fast-Fourier-transform using the filtered-image and a fast-Fourier-transform of the windowed database-image to obtain a correlation-function;

a peak-identifying mechanism configured to identify a peak in the correlation-function; and

a third computing mechanism configured to compute the translational differentials based on location of the identified peak.

33. The apparatus of claim 30, wherein the second computing mechanism includes:

a candidate-computing mechanism configured to compute a set of candidate-translational-differentials using the database-image and the scanned-image;

a gradient-image-generating mechanism configured to generate one or more sets of translated directional-gradient-images based on the set of candidate-translational-differentials and using the database-image and the scanned-image;

a image-converting mechanism configured to convert the database-image into a set of smoothed directional-gradient-images; and

a differential-computing mechanism configured to compute the translational differentials by performing a normalized correlation using the set of smoothed directional-gradient-images and the one or more sets of translated directional-gradient-images;

wherein computational time is significantly reduced because the method performs normalized correlation using the set of candidate-translational-differentials, instead of exhaustively performing normalized correlation using all possible translational differentials.

34. The apparatus of claim 33, wherein the candidate-computing mechanism includes:

a second image-converting mechanism configured to convert the database-image and the scanned-image into a database-gradient-image and a scanned-gradient-image, respectively;

a vector-computing mechanism configured to compute database-projection-vectors from the database-gradient-image and scanned-projection-vectors from the scanned-gradient-image by taking orthogonal projections along a set of directions;

a vector-extracting mechanism configured to extract correlation-vectors from the computed database-projection-vectors;

a vector-mapping mechanism configured to map the scanned-projection-vectors to obtain accumulator-vectors in an accumulator space by using the correlation-vectors; and

a second candidate-computing mechanism configured to compute a set of candidate-translational-differentials based on peak-cluster locations in the accumulator space, wherein a peak-cluster is a collection of contiguous elements around a peak (including the peak).

35. The apparatus of claim 34, wherein the second image-converting mechanism includes:

a filter-creating mechanism configured to create a directional-gradient filter using the database-image, wherein the directional-gradient filter can be used to attenuate edgels that do not conform to directional gradients of feature edges in the database-image;

a third image-converting mechanism configured to convert the database-image and the scanned-image into a set of database directional-gradient-images and a set of scanned directional-gradient-images, respectively;

an image-generating mechanism configured to generate a raw database-gradient-image and a raw scanned-gradient-image from the set of database directional-gradient-images and the set of scanned directional-gradient-images, respectively; and

a filter-applying mechanism configured to apply the directional-gradient filter to the raw database-gradient-image and the raw scanned-gradient-image to obtain the database-gradient-image and the scanned-gradient-image, respectively.

36. The apparatus of claim 34, wherein the gradient-image-generating mechanism includes:

a de-projecting mechanism configured to de-project only cluster-peaks in the accumulator-vectors to obtain reconstructed scanned-projection-vectors;

a second de-projecting mechanism configured to de-project the reconstructed scanned-projection-vectors to obtain reconstructed directional-gradient-images; and

an image-generating mechanism configured to generate one or more sets of translated directional-gradient-images by displacing the reconstructed directional-gradient-images using the set of candidate-translational-differentials;

wherein de-projecting only the cluster-peaks improves signal-to-noise ratio of the reconstructed directional-gradient-images.

37. The apparatus of claim 35, wherein the filter-creating mechanism includes:

an image-convolving mechanism configured to convolve the database-image with a horizontal and a vertical Point Spread Function (PSF) to generate a horizontal edgel-image and a vertical edgel-image, respectively;

an image-computing mechanism configured to compute a gradient-magnitude-image using the horizontal edgel-image and the vertical edgel-image;

a second filter-applying mechanism configured to apply a clip-low filter to the gradient-magnitude-image to obtain a clipped-gradient-image;

a histogram-generating mechanism configured to generate a histogram using gradient orientations in the clipped-gradient-image; and

a second filter-creating mechanism configured to create the directional-gradient filter using the histogram.

38. The apparatus of claim 33, wherein the image-converting mechanism includes:

a fourth image-converting mechanism configured to convert the database-gradient-image into a set of unsmoothed directional-gradient-images; and

a third filter-applying mechanism configured to apply a low-pass filter to the set of unsmoothed directional-gradient-images to obtain the set of smoothed directional-gradient-images.

39. An apparatus for computing translational differentials between a database-image and a scanned-image of a photomask, the apparatus comprising:

an image-receiving mechanism configured to receive the database-image that is noise free and the scanned-image that is generated by an imaging process;

a geometry-determining mechanism configured to determine whether the database-image has a complex geometry;

a pattern-determining mechanism configured to determine whether the database-image is a line-and-space pattern;

a differential-computing mechanism, wherein if the database-image is a line-and-space pattern, the differential-computing mechanism is configured to,

convert the scanned-image into a polarity-enhanced-image; and

compute translational differentials by performing a correlation using the database-image and the polarity-enhanced-image;

otherwise, if the database-image is not a line-and-space pattern but has a complex geometry, the differential-computing mechanism is configured to compute translational differentials using a correlation-filter based approach using the database-image and the scanned-image;

otherwise, if the database-image is not a line-and-space pattern and does not have a complex geometry, the differential-computing mechanism is configured to compute translational differentials using an orthogonal-projection based approach using the database-image and the scanned-image;

wherein accuracy of the computed translational differentials is significantly increased because the method chooses a technique for computing the translational differentials which is suitable for a type of pattern present in the database-image.