BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will now be specified with reference to its preferred embodiment illustrated in the drawings, in which:
FIG. 1 shows a schematic view of a typical surface profile measuring apparatus;
FIG. 2 is an interference diagram showing a typical white light interferometry waveform with effective data;
FIG. 3 is an interference diagram showing a waveform with respect to the dark area;
FIG. 4 is a flow-chart of a preferred embodiment of the surface profile measuring method in accordance with the present invention;
FIG. 5 is a schematic view showing a first preferred embodiment of step C in FIG. 4;
FIG. 5A is a flow-chart showing the first preferred embodiment of step C in FIG. 4;
FIG. 6 is a schematic view showing a second preferred embodiment of step C in FIG. 4;
FIG. 7 is a schematic view showing a third preferred embodiment of step C in FIG. 4;
FIG. 7A is a flow-chart showing the third preferred embodiment of step C in FIG. 4;
FIG. 8 is a flow-chart showing a first preferred embodiment to step E in FIG. 4;
FIG. 9 is a flow-chart showing a second preferred embodiment to step E in FIG. 4; and
FIG. 10 is a flow-chart showing a third preferred embodiment to step E in FIG. 4.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 4 is a flow chart depicting a preferred embodiment of the surface profile measuring method in accordance with the present invention, which uses the typical non-contact surface profile measuring apparatus as shown in FIG. 1 to measure the surface profile of a sample surface 90. The beams from the broad bandwidth light source 10 illuminate the sample surface 90 and a reference surface on the reflector 64. In step A, a serial of interference images are accessed by changing the distance between the sample surface 90 and the reference surface (or the interferometer 60) with a predetermined step distance. In step B, interference diagrams showing a relationship of height versus intensity are derived by using the intensity variation of the pixels with the same locations on the interference images. It is noted that every pixels on the interference image has a respected interference diagram.
Afterward, in step C, according to the waveform in the interference diagram to decide whether the respected pixel located in a dark area or not. Then, in step D, the surface profile of the sample surface with marked pixels located in the dark area is formed. Thereafter, in step E, the marked pixels are repaired by using the values of the surrounding effective pixels on the surface profile.
FIG. 2 is an interference diagram showing a typical white light interferometry waveform with respect to the effective pixel on the surface profile, and FIG. 3 shows a waveform of the pixel located in the dark area on the surface profile. As shown, the waveform with respect to the effective pixel has a significant “envelope” and interference fringes, whereas the waveform with respect to the pixel located in the dark area has no “envelope” or even interference fringes. In addition, the highest intensity value with respect to the effective pixel is about 4 times greater than the highest intensity value with respect to the pixel located in the dark area.
Based on the difference of the waveforms in FIGS. 2 and 3, in step C, the highest intensity value on the waveform or the existence of a significant envelope on the waveform, may be used to decide whether the respected pixel located in the dark area or not.
FIGS. 5 and 5A shows a first preferred embodiment of the step C as describe in FIG. 4, which uses the highest intensity value on the waveform to decide whether the respected pixel located in the dark area or not. Firstly, as shown in step 100 of FIG. 5A, the highest intensity values max(I(z)x,y) on the waveforms with respect to every pixels with the same location (x,y) on the interference images are derived.
Then, in step 120, the highest intensity values max(I(z)x,y) of every pixels with the same location (x,y) on the interference images are normalized into a comparing region range between 0 to N as follow:
Normal(max(I(z)x,y))=N×[max(I(z)x,y)−Min(max(I(z)x,y))]÷[Max(max(I(z)x,y))−Min(max(I(z)x,y))] (1)
Where, max(I(z)x,y) is the highest intensity value with respect to the pixels with the location (x,y); Normal(max(I(z)x,y)) is the normalized value of the highest intensity value max(I(z)x,y); Max(max(I(z)x,y)) is the maximum among the highest intensity values of every locations (x,y); and Min(max(I(z)x,y)) is the minimum among the highest intensity values of every location (x,y).
Then, in step 140, a threshold value in the comparing region is selected. As the normalized value Normal(max(I(z)x,y)) being smaller than the threshold value, the respected pixel on the surface profile is regarded as located in the dark area.
The above mentioned method comparing the highest intensity value on the waveform with respect to a threshold value may be understood as selecting a threshold intensity value TB as shown in FIG. 5. As the highest intensity value being smaller than the threshold intensity value TB, the respected pixel on the surface profile may be regarded as located in the dark area. In addition, the threshold intensity value TB may be ranged between 0 to 75% of the maximum among the highest intensity values as a preferred embodiment in accordance with the present invention.
Except the method of using the highest intensity values on the waveforms directly, FIG. 6 shows a second preferred embodiment of the step C, which pre-operates the function I(z) of the waveform accessed in step B to derive a first differential function I′(z) to decide the position of the highest intensity value on the waveform. The first differential function I′(z) may be understood as a function describing the difference between intensity values I(z) and I(z−1). Then, find out the maximum value max([I′(z)]2) on the squared first differential function. As the maximum value max([I′(z)]2) being smaller than a selected threshold value T2, the respected pixel may be regarded as located in a dark area. Ordinarily, the maximum value max([I′(z)]2) and the greatest intensity value max(I(z)x,y) are respected to an identical height z.
FIGS. 7 and 7A shows a third preferred embodiment of the step C as shown in FIG. 4, which decides whether the pixel located in the dark area according to the existence of a significant “envelope” on the waveform in the interference diagram. Firstly, in step 200, a predetermined width of envelope L is selected according to the width of existed envelopes on the waveforms. The number of scans, or the number of respected interference images, with respect to the predetermined width of envelope is calculated according to the step distance.
Then, in step 220, sum up the absolute first-order differential values of intensity with respect to all the scans on the waveform to access a value of whole scan E(x,y). In addition, in step 240, sum up the absolute first-order differential values of intensity with respect to the scans with respect to the predetermined width of envelope to access a value of envelope portion D(x,y).
Afterward, in step 260, a ratio R(x,y) is derived by dividing the value of envelope portion D(x,y) into the value of whole scan E(x,y). Moreover, in step 280, a threshold value ranged between 0 and 1 is selected. As the ratio R(x,y) being smaller than the threshold value, the respected pixel is regarded as located in the dark area and marked.
After marking the pixel located in the dark area on the surface profile, different embodiments of the step E as shown in FIG. 4 for repairing various distributions of dark areas are provided in the present invention.
FIG. 8 shows a first preferred embodiment of the method for repairing the dark area as described in the step E. As shown, for a given marked pixel 1 located in the dark area, the average value of the adjacent effective pixels N1, N2, N3, N4, and N5 are used to repair the marked pixel 1. The present repairing method starts with the marked pixel 1 and steps inward the dark area (as the increasing of the pixel number implies). That is, the present embodiment repairs the dark area from the marked pixels located in the intersection between the marked pixels and the effective pixels and steps toward the inner of the dark area.
FIG. 9 shows a second preferred embodiment of the method for repairing the dark area as described in step E of FIG. 4. As shown, the marked pixel C within the dark area is repaired by using the values of two nearest effective pixels A,B in the opposite directions from the marked pixel C and the distances a,b between the effective pixels A,B and the marked pixel C. The value of the marked pixel C is derived according to the equation as follow:
V(C)=V(A)+(V(B)−V(A))×a÷(a+b) (2)
Where, V(A) and V(B) are the values of effective pixels A and B respectively; V(C) is the value utilized for repairing the marked pixel C; and a and b are the distances between the marked pixel C and the effective pixels A and B respectively.
FIG. 10 shows a third preferred embodiment of the method for repairing the marked pixel as described in step E of FIG. 4. In compared with the method of FIG. 8, which uses the effective pixels A, B located along a longitude axis to repair the marked pixel C, the present embodiment repairs the marked pixel C by using the values of effective pixels Ai, Bi located along four axes Xi including a longitude axis, a vertical axis, and two tilting axes, which make an 45 degrees with the longitude axis (i=1˜4).
Since the distances between the marked pixel and the effective pixels as well as the values of the effective pixels along the four axes Xi may be different. The weight of each axis Xi should be concerned as follow:
W(i)=|V(Ai)−V(Bi)|÷(ai+bi);
Where, V(Ai) and V(Bi) are the values of nearest effective pixels Ai and Bi in the opposite directions along axis Xi with respect to the mark pixel C; and ai and bi are the distances from the marked pixel C to the effective pixels Ai and Bi respectively. Four weights W(i) respecting to the four axes Xi (i=1˜4) are derived.
The respected weight w(i) along each axis Xi is calculated as follow:
w(i)=W(i)+(W(1)+W(2)+W(3)+W(4));
Where, w(i) is the respected weight of axis Xi; and W(i) is the weight with respect to the axis Xi (i=1˜4).
Then, apply the respected weight w(i) into equation (2) as follow:
V(Ci)=[V(Ai)+(V(Bi)−V(Ai))×a÷(ai+bi)]×w(i) (3)
The equation (3) is utilized to access four contribution values V(Ci) of the four axes Xi (i=1˜4). The four contribution values V(Ci) are summed up to access the exact value for repairing the marked pixel as follow:
V(C)=V(C1)+V(C2)+V(C3)+V(C4) (4)
In compared with the traditional method of filtering the error messages of the surface profile data due to poor surface reflectivity, the present invention marks the pixel in the dark area on the surface profile by using the waveform in the interference diagram, which is accessed before the surface profile data being derived. In addition, the marked pixels on the surface profile may be effectively repaired by using the values of effective pixels surrounding the marked pixels. As s result, the problems encountered by the traditional repairing method due to the lack of location and characteristic information of the dark area may be prevented.
While the embodiments of the present invention have been set forth for the purpose of disclosure, modifications of the disclosed embodiments of the present invention as well as other embodiments thereof may occur to those skilled in the art. Accordingly, the appended claims are intended to cover all embodiments which do not depart from the spirit and scope of the present invention.
Patent Application
20080013101
