Image analysis – Histogram processing
Reexamination Certificate
2000-10-04
2004-05-18
Johns, Andrew W. (Department: 2621)
Image analysis
Histogram processing
C382S172000
Reexamination Certificate
active
06738511
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates to optical metrology, and particularly to the use of interferometry to measure the surface profile of an object with reduced noise sensitivity.
In the use of interferometry to measure the surface profile of an object, the object is illuminated with a reference light beam and the light reflected from the object is caused to interfere with the reference beam so as to produce a two-dimensional interference pattern, or “interferogram.” The interferogram is a function of the two-dimensional distribution of the phase difference between the reference and reflected beams, or “phase map.” Since the phase map depends on the optical path difference (“OPD”) between those beams, it represents a two-dimensional map of the surface profile of the object.
The interferogram is a two-dimensional distribution of light intensity which varies as follows:
I
(
x
,
y
)
=
w
r
(
x
,
y
)
+
w
t
(
x
,
y
)
&RightBracketingBar;
2
=
a
2
+
b
2
+
2
(
ab
)
1
2
cos
2
k
[
s
(
x
,
y
)
-
l
]
=
1
+
γcos
[
φ
(
x
,
y
)
]
where w
r
(x,y)=ae
2ikl
, the reference wavefront,
w
t
(x,y)=be
2iks(x,y)
, the wavefront reflected from the object under test,
k
=2&pgr;/&lgr;
&lgr; is the wavelength of the light,
l is an arbitrary measure of the reference beam path length,
s(x,y) is the surface profile of the object under test,
y=2ab/(a
2
+b
2
), the interference fringe visibility, and
&phgr;(x,y) is the phase difference between the reference beam and the beam reflected from the object under test due to variations in the surface profile of the object.
Since the reference wavefront is considered to be flat and l is fixed, variations in the surface profile of the object under test, s(x,y), are proportional to the phase difference between the test and reference beams, &phgr;(x,y), and an arccosine function of variations in the intensity of the interference fringes, I(x,y).
Often the average surface height of the object under test is not parallel to the reference beam wavefront. This introduces a linear component in phase difference, &phgr;(x,y), which is known as tilt. It is often desirable to remove the tilt from phase difference measurements as a step in calculating the surface profile from the phase difference measurements.
Typically, the interferogram is imaged onto a video camera or CCD array, which is used to produce a two-dimensional array of measurement points, or pixels. A corresponding two-dimensional array of phase map pixels, &phgr;(x
i
,y
j
), is then produced using one of a variety of known methods. The surface profile is calculated from this array of pixels. A system for performing this process is described, for example, in Wyant et al., U.S. Pat. No. 4,639,139, entitled OPTICAL PROFILER USING IMPROVED PHASE SHIFTING INTERFEROMETRY (“Wyant et al.”), hereby incorporated by reference in its entirety.
A problem in determining the surface profile from the phase map, &phgr;(x
i
,y
j
), is that the cosine function repeats, or wraps around, every 2&pgr; radians of phase difference, that is, every wavelength, &lgr;, units of OPD. So, for example, one cannot tell the difference between cos &pgr;/4 and cosine 5&pgr;/4. Since one wavelength of the light used to produce the interferogram is often less than the cumulative variations in object surface height from one pixel to the next, sometimes even less than the change in surface height between one pixel and the next pixel, and often less than the difference in OPD introduced by tilt, it is necessary to account for the discontinuities caused by the aforedescribed wrapping. Doing so is called “unwrapping.”
Another problem in determining the surface profile from &phgr;(x
i
,y
j
) is that both the discontinuities caused by wrapping and the sampling to produce pixels, as well as other random variations in the phase difference data, produce noise in the phase map, &phgr;(x
i
,y
j
), which can produce measurement errors. It is desirable to reduce the sensitivity to that noise.
There are several methods used to calculate a surface profile map from a phase difference map. They differ mainly in the way that they handle noise.
One such method, sometimes referred to as “standard integration”, scans through the phase data consecutively and removes each half-wave discontinuity as it is encountered by adding or subtracting 2&pgr; radians of phase to the adjusted previous adjacent pixel to adjust the phase of the current pixel, if needed. This step is adequate as long as there is no noise and the phase difference between adjacent pixels is less than 2&pgr; radians. However, there usually is noise, and discontinuities greater than 2&pgr; radians may be introduced by discontinuities in surface height, and regional under sampling of the fringe pattern, that is, where the sample frequency is such that the absolute value of the phase difference between two pixels is 2&pgr; radians or more. In the case of discontinuities additional steps must be taken, such as those described in D. Malacara, et al.,
Interferogram Analysis for Optical Testing
, pp. 381-407 (1998). After the phase is unwrapped, tilt is then removed.
A problem with standard integration is that noise tends to propagate from one pixel to the next. This is because each phase adjustment is made with respect to the next preceding pixel. Thus, if there is a noise error in a pixel, that error will affect all of the subsequently evaluated pixels.
In standard integration, noise is reduced by relying on the fact that high noise data typically has a low modulation value. By raising the modulation threshold, most of the noise can be eliminated. The modulation value is the term 2(ab)
½
in the interferogram intensity pattern equation shown above.
Another method for unwrapping, commonly known as “enhanced integration”, uses the standard integration steps but adds some data processing to reduce noise that gets through despite raising the modulation threshold. Errors in this method normally result in a streak of pixels running in the x or y direction at the wrong height.
In yet another method for unwrapping, commonly known as “roughness filtering,” the phase data is first separated into “rough,” “smooth,” and “cliff” categories, then treated according to its category. This categorization is accomplished by comparing height differences between adjacent pixels to empirically obtained standards. Cliff data is that which represents at least a halfwave discontinuity. Smooth data is noise free. Rough data does not fit into either of the other two categories and is ignored.
In the measurement of the surface contour of relatively flat surfaces, such as the surfaces of a magnetic disk recording head, noise is the prevalent problem. Surface height variations do not tend to exceed one-half wavelength, though tilt is typically present, but noise often causes a discontinuity to be introduced during the unwrapping. It has been found that because the aforementioned unwrapping methods adjust the phase based on the next-preceding pixel, they are sensitive to noise and produce errors in measuring the surface contour of such relatively flat objects. Therefore, there is a need for reduced noise sensitivity method and apparatus for converting an interferogram phase map to a surface profile map.
SUMMARY OF THE INVENTION
The present invention addresses the aforementioned phase unwrapping problem and meets the aforementioned need for reduced noise sensitivity in the measurement of the contour of objects, particularly relatively-flat objects.
Assuming either that the phase data has no significant tilt or that the phase data has been adjusted to remove phase discontinuities due to tilt, a histogram is created from the phase data wherein the bins of the histogram represent phase values from zero to 2&pgr; radians relative to a reference beam and the items in the bins represent occurrences of respective phase values in the phase data. Useful phase data is then identified by selecting groups
Farrell Colin T.
Herron, Jr. Jon D.
Alavi Amir
Birdwell William A.
Durando Birdwell & Janke PLC
Johns Andrew W.
Veeco Instruments Inc.
LandOfFree
Reduced noise sensitivity method and apparatus for... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Reduced noise sensitivity method and apparatus for..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reduced noise sensitivity method and apparatus for... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3256633