 |
Description  |
|
|
FIELD OF INVENTION
The present invention relates to an optical interferometric measurement
method and apparatus with greatly reduced sensitivity to measurement
errors produced not only by the presence of vibrations in the environment
but also instrument phase shifting inaccuracies.
BACKGROUND OF THE INVENTION
An overview of interferometric techniques used in the prior art is provided
by J. E. Greivenkamp and J. H. Bruning in Chapter 14 of "Optical Shop
Testing", 2nd Ed., J. Wiley pub, edited by D. Malacara. These techniques
are used extensively for high precision, non-contact metrology. With
careful control of environmental conditions, measurement precision to the
nanometer scale or below is possible with these techniques; however,
residual measurement errors may occur, with external vibration being the
single largest cause of such residual measurement errors. For most
commercial profilers, control of environmental conditions requires, at a
minimum, a passively isolated instrument; however, passive vibration
isolators perform poorly against low frequency vibrations. Prior art
attempts at solving these problems have not been completely satisfactory
with having involved such approaches as changing the phase extraction
algorithm, as disclosed in articles by P. de Groot, "Vibration in phase
shifting interferometry", J. Opt. Soc. Am. A 12, 354-365 (1995), C. T.
Farrell and M. A. Player, "Phase-step insensitive algorithms for
phase-shifting interferometry", Meas. Sci. Tech. 5, 648-652 (1994), and I.
Kong and S. Kim, "General algorithm of phase-shifting interferometry by
iterative least-squares fining", Opt. Eng. 34, 183-188 (1995). This prior
art approach, while not completely satisfactory, can provide some useful
reduction in vibration sensitivity. The prior art approaches suggested by
Farrell and Player, and more recently Kong and Kim, show significant
insensitivity to small amplitude vibrations if the phase shift is assumed
to be constant across the field and a least squares fit to this constraint
is performed in the analysis of the interferogram. Large amplitude
vibrations, however, can make it impossible to overcome a phase ambiguity
in the analysis that the authors attempt to currently resolve by assuming
the phase shifts are unidirectional. Another prior art approach, which is
not completely satisfactory as well, is discussed in an article by J. L.
Seligson, C. A. Callari, J. E. Greivenkamp, and J. W. Ward entitled
"Stability of a lateral-shearing heterodyne Twyman-Green interferometer",
Opt. Eng. 23, 353-356 (1984) in which the authors discuss using a separate
interferometer to measure the true phase shifts during interferogram
acquisition. This, in principle, can substantially reduce vibration
sensitivity even for large amplitude disturbances, but it is expensive and
difficult to implement, requiring a stabilized laser, precision optics and
sophisticated electronics to measure the true motion of the phase shifter.
As a laboratory tool it may suffice, however, it is not a commercially
viable solution. Another prior art approach, with results similar to those
discussed in Seligson is disclosed in U.S. Pat. No. 5,410,405, to Schultz
et. al. which discloses using a homodyne interferometer to achieve similar
motion measurements as Seligson above. Recent work on the vibration
sensitivity of various algorithms, such as discussed in the above de Groot
article, shows, however, that all algorithms will be most sensitive to
vibrational frequencies at half the data acquisition rate since vibrations
at this frequency produce phase variations which are indistinguishable
from phase variations due to surface features. The sampling rates are
driven by video with cameras most often being used to sample the
interferogram, and that makes 30 Hz very typical: thus vibrations at 15 Hz
and lower cause the bulk of the problems. Active vibration compensation
devices, such as commercially available from Newport Corp. (Irvine Calif.)
are expensive and can compensate for only a limited vibration amplitude
range, and do not correct for deficiencies in the apparatus itself, such
as scanning nonlinearities. Another prior art approach is discussed in a
paper presented by J. A. Meiling, entitled "Interferometric Metrology of
Surface Finish Below 1 Angstrom RMS", which appears in the April 1992
proceedings of the ASPE spring topical meeting on precision
interferometric metrology. In this paper Meiling presented results based
on massive data averaging. This methodology, however, is extremely slow
and systematic errors will not average out.
Another prior art approach, called instantaneous phase detection, such as
described by R. Smythe and R. Moore, in "Instantaneous phase measuring
interferometry", Opt. Eng. 23, 361-364 (1984) and in U.S. Pat. Nos.
4,653,921 and 4,624,569 to Kwon, is fast, thereby "freezing out" the
vibration effects however, it requires a minimum of 3 detectors (typically
four to achieve resolutions typically expected for an interferometric
instrument) and these detectors must be prealigned spatially to sub-pixel
accuracy and have the identical environmental characteristics if the
operating conditions are not to be too restrictive. The image must be
split between each detector and the phase shifted optically with a phase
retarder, whose retardation must be either uniform across the field or
known as a function of field. The individual pixel gains and offsets of
each detector must be either identical (almost impossible) or mapped; and
the images must also be acquired simultaneously, requiring the equivalent
of 3 or 4 framegrabbers all synchronously operated. These problems and the
associated costs make this prior art method extremely difficult to
implement beyond single point detection applications described in the
articles cited.
The practical difficulties of increasing the speed of data acquisition have
even made even this apparent "straightforward" method relatively
difficult, especially since profiling applications rarely wish to
sacrifice lateral resolution for speed. High speed, high resolution
sensors are rare and extremely expensive. For example, a 210 Hz, 1024
pixel.times.1024 pixel, camera produced by the David Sarnoff Labs (the SAR
1024) has 32 parallel output taps and costs over $200,000. The high speed
requirement directly impacts the camera signal to noise ratio, forcing
most of these cameras into a multiple output (multitapped) configuration.
The multitapped nature of these cameras then requires a sophisticated data
acquisition device that is incompatible with typical commercial
framegrabbers. A custom acquisition system for the SAR 1024 called the RAM
CUBE was built by TRW and costs as much as the camera. Although, other
commercially available high speed, high resolution cameras may be less
costly, it has been found that incorporating high speed, high resolution
cameras into practical commercially viable products at the present time,
apart from any other problems, is simply not cost effective.
The present invention overcomes these problems in the prior art and allows
the use of inexpensive low frame rate, high density cameras to achieve
vibration insensitivity almost as good as that achievable with a single
camera of comparable density and speed. Furthermore, the presently
preferred method of the present invention is applicable to many different
types of interferometric systems, such as phase shifting interferometers,
coherence scanning interferometers or long equivalent wavelength
interferometers. In addition, the presently preferred method of the
present invention is also capable of correcting for instrumental
deficiencies, such as errors in the phase shifting apparatus, without the
need for additional distance measuring interferometers, thereby reducing
cost.
SUMMARY OF THE INVENTION
In accordance with the presently preferred method and apparatus of the
present invention, the interference pattern, i.e. interferogram, generated
by an interferometer is amplitude split to form two interferograms, one of
which is imaged onto a first detector and the second of which is imaged
onto a second detector. The two detectors preferably have different frame
rates, i.e. data acquisition rates. Typically, preferably the fast frame
rate detector has a low pixel density and the slow frame rate detector has
a high pixel density.
In accordance with the present invention, in a phase shift interferometric
(PSI) type of measurement, such as is typically used for the topological
profiling of surfaces, the high frame rate detector acquires a sequence of
interferograms, referred to as the fast data set, during the data
acquisition such that the phase separation between sequential
interferograms is nominally 90 degrees. The low frame rate detector is
preferably synchronized to the high frame rate detector so as to acquire a
sequence, i.e. the slow data set, of interferograms with the identical
frame integration time but at a lower frequency. The fast data set is then
preferably analyzed for the phase for each interferogram using a
conventional phase shift interferometry algorithm, and the phase
difference between interferograms in the slow data set is determined from
the phases derived from the fast data set. The slow data set is then
preferably analyzed for the surface profile, with the phase differences
obtained from the previous step above by a generalized phase shift
interferometry algorithm which can account for non-equal phase separations
between interferograms. In accordance with this presently preferred
method, the phase separation between acquired interferograms may be
dynamically measured which enables the correction of heretofore unknown
phase errors due to instrument inaccuracies and the presence of external
vibrations to be readily accomplished in a practical and commercially
viable manner.
In a scanning, short coherence type of interferometric measurement,
referred to as SWLI for Scanning White Light Interferometry, surface
topology measurements also benefit front the ability of the present
invention to dynamically measure the phase difference between
interferograms. One SWLI method involves the dynamic computation of the
contrast function and an immediate or subsequent search for the contrast
peak. Using the dynamically measured phase difference method of the
present invention in the contrast calculation reduces errors in the
computed contrast function due to instrument inaccuracies or external
vibrations thereby facilitating the peak determination. Another SWLI
method involves interferogram capture and subsequent analysis in the
frequency domain. By using the dynamically measured phase difference
method of the present invention and performing, for example, a general
Fourier transform on the interferogram data rather than a fast Fourier
transform, the analysis can be made less susceptible to instrument
inaccuracies and external vibrations.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of a small aperture configuration in
accordance with the presently preferred method and apparatus of the
present invention;
FIG. 2 is a schematic diagram, similar to FIG. 1, of a large aperture
configuration in accordance with the presently preferred method and
apparatus of the present invention;
FIG. 3 is a typical illustrative frame acquisition tinting diagram useful
in explaining the presently preferred method of the present invention;
FIG. 4 is an illustrative graphical illustration of RMS phase errors vs
vibrational frequency for standard Phase Shifting Interferometry useful in
explaining the presently preferred method of the present invention;
FIG. 5 is a graphical illustration, similar to FIG. 4, of RMS phase errors
vs. vibrational frequency for low frequency vibrations; and
FIG. 6 is a graphical illustration, similar to FIG. 4, of RMS phase errors
vs. vibrational frequency for medium frequency vibrations.
FIG. 7 is a graphical illustration, similar to FIG. 4 of RMS phase errors
vs. vibrational frequency for medium frequency vibrations using chirped
acquisition.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Returning now to the drawings in detail and initially to FIG. 1, the
presently preferred apparatus for a small aperture configuration capable
of carrying out the presently preferred method of the present invention is
shown. In accordance with this preferred embodiment, a source of
illumination 34 is provided for producing a beam of light 31 that enters a
conventional interferometer, shown here for example as an interferometric
objective 35, having a reference path and test path. A conventional phase
shifting apparatus which may, by way of example, be an actuator such as a
piezoelectric actuator 45, is preferably provided to vary the length of
one of the interferometer paths by a controlled amount. The interferogram
produced by the recombination of the beams from the two paths of the
interferometer 35 is preferably amplitude split by a beam splitter 33 to
form two interferograms one of which is preferably imaged onto a first
detector 10 and the second of which is preferably imaged onto a second
detector 11. The detectors which may preferably be cameras by way of
example, could be, for example, charge coupled device (CCD) cameras.
Preferably, on the above example, the two cameras have different frame
rates, i.e. data acquisition rates. Typically, the fast frame rate camera
11 preferably has a low pixel density and the slow frame rate camera 10
preferably has a high pixel density. Preferably, the cameras are so
disposed such that the image fields substantially overlap and are
synchronized with each other so that the frame integration periods are
identical and overlap in time. This can, for example, preferably be
accomplished with an external shutter 14 in front of the slow camera 10. A
narrow band filter 17 in front of the fast frame rate camera 11 may
preferably be used primarily to increase the scan range for which high
contrast interference is observed, although its inclusion is optional and
depends on the illumination source 30 coherence properties.
Referring now to FIG. 2, a presently preferred apparatus in accordance with
the present invention, for a large aperture configuration is shown. In
accordance with this preferred embodiment, a source of illumination 30,
shown here as a laser, most preferably a laser diode, is provided for
producing a beam of light 31 that enters a conventional interferometer
having an interference cavity 38 consisting of reference surface 37 and
object 40. A conventional phase shifting apparatus is provided, which may
be a piezoelectric actuator as was the case in the embodiment of FIG. 1,
or preferably, for this configuration, it may be provided by modifying the
laser diode pump current to vary the laser wavelength by a controlled
amount as taught by commonly owned U.S. Pat. No. 4,594,003 to Sommargren.
The interferogram produced by the recombination of the beams from the two
paths of the interferometer is preferably amplitude split by a beam
splitter 33 to form two interferograms one of which is preferably imaged
onto a first camera 10 and the second of which is preferably imaged onto a
second camera 11. The two cameras preferably have different frame rates,
i.e. data acquisition rates. Typically, the fast frame rate camera 11
preferably has a low pixel density and the slow frame rate camera 10
preferably has a high pixel density. The cameras are preferably so
disposed such that the image fields substantially overlap and are
synchronized with each other so that the frame integration periods are
identical and overlap in time. This can, for example, preferably be
accomplished with an external shutter 14 in front of the slow camera 10.
During data acquisition the phase shifter 45 preferably changes the phase
difference between the beams in the interferometer in an approximately
linear fashion while data from both cameras 10 and 11 is taken by a
conventional framegrabber 15 and saved in a computer 25. The data from the
fast frame rate camera 11 is called the fast data set and the data from
the slow frame rate camera 10 is called the slow data set. The rate of
phase change is preferably controlled such that nominally 90 degrees of
phase change occurs between frames in the fast data set. Alternatively,
preferably phase stepping could be implemented whereby nominally 90
degrees of phase change occurs between phase steps. Data acquisition
preferably proceeds until a predetermined number of slow camera 10 frames
are taken. The camera data acquisition rates are at least 2:1.
FIG. 3 illustrates a typical example of an acquisition where the fast
camera 11 has a frame rate 5 times faster than the slow camera 10 and the
slow data set consists of 5 equally spaced frames. The primary fringe
pattern 50 is illustrated in FIG. 3 and is the top sinusoidal pattern.
Fast camera 11 frame acquisitions in the example of FIG. 3 occur every 90
degrees of phase, identified by the boxes labeled 1 through 25. The slow
camera 10 in the FIG. 3 example, only acquires data in the regions marked
by the shaded boxes. Fast camera data is preferably required a few frames
before the first slow camera frame (marked as leader frames) and after the
last slow camera frame (trailer frames) to assure that the phases for
those frames can be calculated with the chosen algorithm.
During data analysis, the phase at each image point on each frame of the
fast data set is preferably calculated by the computer 25 using a
conventional phase extraction algorithm, such as for example, the well
known 5 point algorithm first introduced by Schwider et. al. in "Digital
wave-front measuring interferometry: some systematic error sources", Appl.
Opt. 22, 3421-3432 (1983). These phases are then preferably unwrapped to
remove 2.pi. discontinuities inherent in the algorithm implementation,
thereby providing a smoothly varying measurement of the phase variation
produced by the phase shifter 45 plus environmental effects like
vibrations as a function of field. The phase increment between each frame
in the slow data set is preferably calculated using either the measured
phase variation from the nearest neighbor field point in the fast data
set, or some interpolation thereof. The slow data set is then preferably
analyzed for phase at each image point with, for example, a generalized
least squares algorithm as described by Greivenkamp (J. E. Greivenkamp,
"Generalized data reduction for heterodyne interferometry", Opt. Eng.
23,350-352 (1984)), using these measured phase increments. These phases
are then preferably transformed into physical surface heights of the
object 40 using the light beam 31 mean wavelength.
FIG. 4 illustrates the RMS phase error normalized to the vibrational
amplitude of pure sinusoidal vibrations as a function of the ratio of the
vibration frequency to camera frame rate. In the example of FIG. 4,
standard PSI analysis with the Schwider 5 point phase extraction algorithm
was used, although for PSI a 3 point algorithm could also be used. The
example of FIG. 4 provides a convenient way of categorizing vibrations
into low, medium and high frequencies. Low frequency vibrations are
defined as being inside the first PSI sensitivity peak, i.e. frequencies
below 25% of the camera frame rate. Medium frequency vibrations are
contained inside the main central peak (between 25% and 75% of the camera
frame rate) and high frequencies are all frequencies above that. FIG. 4
illustrates a typical computer simulation of the vibration sensitivity of
the preferably preferred method of the present invention and shows the
reduction in sensitivity to low frequency vibrations when the method of
the present invention is employed with a fast:slow camera ratio of 5:1.
The results are compared in FIG. 5 with standard PSI acquired at a rate
equal to the slow camera rate. In the example of FIG. 5, the Schwider 5
point phase extraction algorithm was used to determine both the fast data
set phases and the standard PSI results. The curve labeled PSI in FIG. 5
represents the RMS error obtained using standard PSI while the curve
labeled HSPSI (High Speed PSI) represents a standard phase shifting
analysis on data acquired at the fast camera rate. Two other curves, 2C-5
and 2C-11, in FIG. 5 represent the RMS phase error using the method of the
present invention, with the number after the dash representing the size of
the slow data set used in the example of FIG. 5. As shown and preferred,
the reduction in vibration sensitivity is substantial over the full range
of low frequencies and is at least as good as acquiring at high speed.
FIG. 6 illustrates an example of the improvement that the method of the
present invention provides for medium vibrational frequencies. The
improvement, though poorer than a high speed acquisition, is still
substantially better than standard PSI at the slow acquisition rate.
Higher frequencies are relatively easy to attenuate with passive
isolators. Further sensitivity reduction at medium frequencies can be
obtained at the cost of raising the high frequency sensitivity by chirping
the acquisition. This is shown by way of illustration, in FIG. 7. To
produce the curves 2C-5Chirp and 2C-11Chirp, illustrated in FIG. 7, the
phase difference between adjacent slow data acquisitions was successively
increased by 90 degrees. This ability to tailor the acquisition to provide
the best vibration suppression for a particular environment is a further
benefit of the present invention.
The maximum size of the slow data set depends on available memory in
computer 25 and the maximum scan range of the phase shifter 45. Increasing
the data set size generally has the effect of narrowing the sensitivity
peaks, such as the one located at half the frame rate. This can be
observed in FIG. 6.
The present invention improves upon prior art methods of providing
vibration insensitivity for optical interferometric profilers by cost
effectively measuring the effects of vibration on the interferometric
phase at one or more points in the field. The phase separation between
data points is a measured quantity rather than an assumed constant as is
typically done in the prior art. In this manner the spectrum of vibrations
that could effect the phase determination is shifted towards higher
frequencies, which are more easily attenuated with passive isolators and
have generally reduced amplitudes. The present invention provides this
improvement for both large and small amplitude vibrations. In addition,
the presently preferred method of the present invention automatically
provides corrections for phase shifter nonlinearities as well. This has
long been realized to be a major source of error in phase shifting
measurements as was pointed out in a prior art article by J. van
Wingerden, H. J. Frankena and C. Smorenburg, titled "Linear approximation
for measurement errors in phase shifting interferometry", Appl. Opt. 30
2718-2729 (1991) and also by K. Kinnstaetter, A. W. Lohmatm, J. Schwider
and N. Streibl, in "Accuracy of phase shifting interferometry", Appl. Opt.
27, 5082-5089 (1988). The fact that the preferred method of the present
invention is capable of utilizing the same interferometric apparatus used
for the surface topology measurements provides a significant cost
reduction relative to prior art methods. Commercial off-the-shelf cameras
and frame grabbers can be used in the method of the present invention
rather than specialized, and costly, detectors or framegrabbers. The
presently preferred method also does not require in most applications,
that the sampling density of the high speed camera 11 be very high because
the phase variation due to vibrations is often common across the aperture.
For microscopes, for example, by using the method of the present
invention, the entire aperture can be corrected by measuring the phase
variation at high rates from a single point in the aperture. The fast
camera could, therefore, be replaced by a single photodiode. For large
aperture interferometers measuring compliant objects, by using the method
of the present invention, the aperture could be large enough to
accommodate more than one spatial vibrational mode and the phase
variations could then be a function of aperture. In these cases it is
necessary to sample the aperture at a spatial density high compared to the
highest expected spatial vibrational period. For most cases of interest
only the low order vibrational modes are excited with any appreciable
amplitude, so again the sampling density of the high speed camera 11 need
not be very great.
Consequently, the presently preferred method and apparatus of the present
invention overcomes many of the disadvantages of the prior art in
providing a practical, and commercially viable solution to the problem of
providing optical interferometric measurement having reduced sensitivity
to measurement errors, such as provided not only by the presence of
vibration sources in the environment, but by instrument phase shifting
inaccuracies as well.
* * * * *
|
|
 |
|
 |
Description |
|
