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Description  |
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FIELD OF THE INVENTION
This invention relates generally to optical metrology and, in particular,
to optical metrology apparatus and method that employs two synthetic
wavelengths and an optical wavelength to obtain sub-nanometer measurement
resolution.
BACKGROUND OF THE INVENTION
One known method to extend the range of optical metrology applications for
interferometry is to measure the interferometric phase at two distinct
wavelengths.
When monochromatic light is made to interfere with itself in a two-beam
interferometer, the output intensity as measured by a square-law detector
is proportional to a function h:
h(mx)=cos.sup.2 (.pi.m), (1)
where m is a real number, referred to herein-as the fringe order, equal to
one over 2.pi. times the relative phase of one beam to the other. The
optical path difference between the two beams is related to the fringe
order by
L=m.lambda./2, (2)
where L is the one-way optical path difference, including the refractive
index, and .lambda. is the vacuum wavelength. In that h is a periodic
function, the integer part of m cannot be determined by inverting Eq. (1).
Interferometry typically provides only the fractional part f(m) of the
fringe order, with the consequence that only changes of the length L, and
not its absolute value, can be measured directly. This integer
fringe-order ambiguity limits the usefulness of interferometry in many
applications.
The purpose of multiple-color, or multiple-wavelength, interferometry is to
measure the integer part of m so that the entire length L may be directly
measured with great precision in terms of the vacuum wavelength.
Analytical procedures for determining lengths from multiple-wavelength
interferometry exist in a variety of forms. One such procedure employs the
concept of synthetic wavelengths, corresponding to differences in phase
measurements for pairs of wavelengths in the interferometer.
By example, and considering three optical wavelengths .lambda..sub.1,
.lambda..sub.2, and .lambda..sub.3, there are three possible synthetic
wavelengths defined by
1/.LAMBDA..sub.ij =1/.lambda..sub.i -1/.lambda..sub.j,.lambda..sub.j
>.lambda..sub.i. (3)
It is noted that a synthetic wavelength can be made much larger than a
visible wavelength by choosing appropriate pairs of wavelengths
.lambda..sub.i, .lambda..sub.j. The corresponding synthetic fringe orders
M.sub.ij are obtained from the differences in optical fringe orders
m.sub.i and m.sub.j as:
M.sub.ij =m.sub.i -m.sub.j ( 4)
The length L may be calculated from a synthetic wavelength measurement as:
L=(M.sub.ij .LAMBDA..sub.ij)/2. (5)
The larger the synthetic wavelength the greater the range of distances L
that can be accommodated without possibility of error due to an integer
ambiguity in the value of M.sub.ij. Conversely, the precision in the
measurement of L is optimized when using relatively small synthetic
wavelengths.
The following prior art discuss various aspects of conventional
two-wavelength interferometry. As described in U.S. Pat. No. 4,832,489,
issued May 23, 1989, to J. C. Wyant et al., a two-wavelength
phase-shifting interferometer employs two laser sources for reconstructing
steep surface profiles, such as aspheric surfaces. A 256.times.256
detector array is used and the technique computes an equivalent phase
independently for each detector.
The following articles discuss various aspects of employing a synthetic
wavelength for surface profilometry.
In an article entitled "Contouring Aspheric Surfaces Using Two-Wavelength
Phase-Shifting Interferometry" by K. Creath, Y. Cheng, and J. Wyant,
Optica Acta, 1985, Vol. 32, No. 12, 1455-1464 there is described
two-wavelength holography using an argon-ion laser and a He-Ne laser. Two
wavelengths from the argon-ion laser (0.4880 micrometers or 0.5145
micrometers) were employed in conjunction with a single wavelength (0.6328
micrometers) from the He-Ne laser to yield equivalent wavelengths of 2.13
micrometers and 2.75 micrometer. An uncoated test surface was placed in
one arm of the interferometer and interferograms were recorded using a
100.times.100 diode array.
In an article entitled "Absolute Optical Ranging with 200-nm Resolution" by
C. Williams and H. Wickramasinghe, Optics Letters, Vol. 14, No. 11, Jun.
1, 1989 there is described optical ranging by wavelength-multiplexed
interferometry and surface profiling said to be carried out on an
integrated circuit structure. A pair of GaAlAs single-mode diode lasers
are used as optical sources.
In an article entitled "Two-wavelength scanning spot interferometer using
single-frequency diode lasers" by A. J. de Boef, Appl. Opt., Vol. 27, No.
2, Jan. 15, 1988 (306-311) there is described the use of two single
frequency laser diodes to measure the profile of a rough surface. The two
wavelengths are not time-multiplexed but are instead continuously present.
In an article entitled "Two-Wavelength Speckle Interferometry on Rough
Surfaces Using a Mode Hopping Diode Laser" by A. Fercher, U. Vry and W.
Werner, Optics and Lasers in Engineering 11, (1989) pages 271-279 there is
described a time-multiplexed two-wavelength source consisting of a single
mode diode that is switched between two adjacent oscillation modes. The
switching is accomplished by pump-current modulation with the diode
thermally tuned to a region near a so-called "mode hop", that is, near a
region where the diode output readily switches from one wavelength output
to another. This technique is said to have enabled the profiling of a
ground lens surface.
As was previously stated, the larger the synthetic wavelength, the greater
the range of distances (L) that can be accommodated without possibility of
error due to an integer ambiguity in the value of the synthetic wavelength
fringe order (M.sub.ij). However, the precision in the measurement of L is
best when small synthetic wavelengths are used.
It is thus an object of the invention to provide optical metrology
apparatus that employs a plurality of synthetic wavelengths of different
size.
It is a further object of the invention to provide optical metrology
apparatus that employs a plurality of synthetic wavelengths of different
size, the synthetic wavelengths being derived from three optical
wavelengths emitted from two laser diodes, at least one of which is a
multi-mode laser diode.
It is another object of the invention to provide optical metrology
apparatus that employs a plurality of synthetic wavelengths of different
size, using progressively smaller synthetic wavelengths to improve the
precision of measurement while retaining the dynamic range made possible
by a large synthetic wavelength.
SUMMARY OF THE INVENTION
The foregoing and other problems are overcome and the objects of the
invention are realized by method and apparatus for performing optical
metrology. In accordance with a method of the invention, and apparatus for
accomplishing same, a first step generates an optical output having a
plurality of optical wavelengths. A next step modifies the optical output
to provide a phase modulated reference beam and a measurement beam that
are orthogonally polarized with respect to one another. The measurement
beam is directed to and reflects from at least one surface. A further step
combines the phase modulated reference beam and the reflected measurement
beam into a combined beam. A next step detects, in accordance with a
polarization state of three optical wavelengths within the combined beam,
a difference between an optical path length of the reference beam and an
optical path length of the measurement beam. The difference in path
lengths is indicative of an absolute distance L.
The teaching of the invention provides an optical metrology system wherein
three optical wavelengths of a fixed polarization are separated into two
beams (OB and RB) having, ideally, nearly equal optical path lengths. The
two beams are recombined and provided to sensors which measure the
intensity associated with each of the wavelengths.
The teaching of the invention furthermore provides a plurality of multimode
laser diodes for generating three optical wavelengths. Two synthetic
wavelengths are derived from the three optical wavelengths. The synthetic
wavelengths are of different size and progressively smaller synthetic
wavelengths are employed to improve the precision of measurement while
retaining a large dynamic range made possible by the use of a large
synthetic wavelength.
BRIEF DESCRIPTION OF THE DRAWING
The above set forth and other features of the invention are made more
apparent in the ensuing detailed description of the invention when read in
conjunction with the attached drawing, wherein:
FIG. 1 is a simplified block diagram of a three-color interferometer for
performing absolute distance measurement and surface profiling;
FIG. 1a is a graph showing the combined optical spectrum of two multi-mode
laser diodes;
FIG. 2 is a graph depicting a high resolution displacement measurement
performed by the three-wavelength interferometer of FIG. 1; and
FIG. 3 is a graph of a central region of an unsilvered parabolic mirror
obtained with the three-wavelength interferometer of FIG. 1.
DETAILED DESCRIPTION OF THE INVENTION
Referring first to FIG. 1 there is shown a three-wavelength, or
three-color, optical metrology system 1 that is constructed and operated
in accordance with an embodiment of the invention. System 1 includes a
three-wavelength source 10 that includes, preferably, two multimode laser
diodes 12 and 14, collimating optics 12a and 14a, mirrors 12b and 14b, and
an optical isolator 15. The laser diodes 12 and 14 are simultaneously
operated and thus simultaneously provide three wavelengths. The emission
from each laser diode 12 and 14 is transmitted through an optical fiber 16
to phase-modulating, two-beam polarizing interferometer optics 18. A
reflected object beam, also referred to as a measurement beam, and a
reference beam are recombined and transmitted back through the optical
fiber 16 to a diffraction grating 20. Detectors 22, 24 and 26 are
positioned in space to intercept the separated wavelengths provided by the
grating 20, via focussing optics 21, and to measure the intensity of the
three different wavelengths. A processor 28 calculates fringe orders and
determines an absolute distance (L) to the object surface.
As can be seen in the graph of FIG. 1a in the three-wavelength
interferometer system 1 two different wavelengths
(.lambda..sub.1,.lambda..sub.2) in the 785 nm region of the spectrum are
selected to derive a first synthetic wavelength .LAMBDA..sub.12 =720
micrometers, and .lambda..sub.1 is combined with a third wavelength
.lambda..sub.3 from the 815 nm region for generating a significantly
smaller synthetic wavelength .LAMBDA..sub.13 =20 20 micrometers. The laser
wavelength separation required for a .LAMBDA..sub.13 =20 micrometer
synthetic wavelength is 32 nm, which is relatively large when compared to
the 0.3 nm mode separation of a typical laser diode output. Thus, two
diodes are required, with different center wavelengths. In principle,
since only three wavelengths are used, one laser diode may be a multimode
device and the other a single-mode device. However, the use of two
multimode laser diodes is preferred in that undesirable mode hopping
associated with single-mode laser diodes is avoided. Two suitable
multimode laser diodes are Sharp LT010MDO and LT023MDO laser diode
devices.
The optical fiber 16 spatially filters the emissions of the laser diodes 12
and 14 and facilitates the mechanical mounting of the interferometer
optics 18 for different measurement tasks. The source light from the
optical fiber 16 is focussed at the object surface by optical element 17
and is split into an object beam (OB), and into a reference beam (RB).
Reference beam RB is directed, via a reflector 19, to a mirror 18a that is
coupled to a piezo-electrical transducer 18b. The mirror 18a is oscillated
by the transducer 18b and functions to phase modulate the reference beam
RB. Suitable oscillation frequencies in the range of approximately zero to
approximately 1000 Hz may be employed, although the teaching of the
invention is not limited to this range. For example, an electro-optic
device such as a Kerr cell may be employed to achieve significantly
greater rates of oscillation. OB and RB are given fixed orthogonal
polarizations by a polarizing beam splitter 18c. As a result, when the two
beams are recombined into the optical fiber 16 after reflection, the
resultant polarization vector rotates with the phase modulation. The light
from the interferometer optics 18 is transmitted back through the fiber
optic 16 to a polarizing beam splitter 30 at the source end of the optical
fiber 16. The reflected light is analyzed after passing through the beam
splitter 30. The light is separated into its constituent wavelengths by
the diffraction grating 20 such that the individual wavelengths of the
combined optical spectra appear as a series of spatially distinct points
in space. The detectors 22, 24, and 26 are positioned at these spatially
distinct points for detecting the intensity associated with each of the
three wavelengths. The operation of the phase modulator of the
interferometer optics 18 results in a wavelength-dependent and a
phase-dependent amplitude modulation of the radiation.
As can be seen, the teaching of the invention provides an optical metrology
system wherein three wavelengths of a fixed polarization are separated
into two beams (OB and RB) having substantially equal optical path
lengths. The two beams are recombined and provided to sensors which
measure the intensity associated with each of the wavelengths.
Furthermore, the source/detector optics and the interferometer optics may
be mechanically decoupled from one another by the use of the optical fiber
16.
The processor 28 may actively control the phase modulation of the
interferometer optics 18 while recording the intensity measured by the
three detectors 22, 24 and 26. Alternately, the phase modulator may run at
a fixed rate and the processor 28 may employ well known statistical
methods applied over a group of samples. In either case, a suitable phase
demodulation algorithm is used to determine the optical fringe orders (m)
corresponding to the three wavelengths .lambda..sub.i. One suitable phase
demodulating algorithm is known as a five point algorithm and is described
by P. Harihan, B. F. Oreb and T. Eiju in Appl. Opt. 26 2504 (1987). Length
calculations involving Eq.(6), Eq.(7) and Eq.(8), described below, are
performed in software and the results may be displayed to an operator
and/or stored on disk. The change in optical path length is measured by
applying Eq. (2), (6), (7), and (8) after detection of the relative
interferometric phase at each of the three wavelengths.
Although not shown in FIG. 1, the system 1 further includes laser diode
power supplies, thermoelectric coolers, detector amplifiers, a
piezoelectric driver, and an analog input interface that couples the
detector outputs to the processor 28.
In accordance with an aspect of the invention there are considered three
wavelengths .lambda..sub.1 <.lambda..sub.2 <.lambda..sub.3, and two
corresponding synthetic wavelengths .LAMBDA..sub.12 >.LAMBDA..sub.13. The
procedure for measuring an absolute distance L with interferometric
resolution is as follows.
Assuming that L is less than .LAMBDA..sub.12 /4, the integer part of the
synthetic fringe order M.sub.12 is zero, and
M.sub.12 =f(M.sub.12)=f(m.sub.1)-f(m.sub.2). (6)
The fractional parts f(m.sub.i) of the interferometric fringe orders
m.sub.i are obtained by inverting Eq. (1) or by performing some equivalent
phase-detection algorithm. A next step uses the shorter synthetic
wavelength .LAMBDA..sub.13 to increase the precision in the measurement.
The following equation makes use of M.sub.12 in calculating M.sub.13
without an integer ambiguity:
M.sub.13 =f(M.sub.13)+I((M.sub.12 .LAMBDA..sub.12
/.LAMBDA..sub.13)-f(M.sub.13)). (7)
The function I(a) appearing in Eq.(7) yields the integer nearest to the
argument a. The optical fringe order m.sub.1 is now calculated from
m.sub.1 =f(m.sub.1)+I((M.sub.13 .LAMBDA..sub.13
/.lambda..sub.1)-f(m.sub.1)). (8)
The final step employs Eq.(5) to determine the distance L. The measurement
of L is thus accomplished as a three-step process, wherein M.sub.12 is
used to remove the integer fringe order ambiguity in the calculation of
M.sub.13, and M.sub.13 is used in the calculation of m.sub.1. This
technique results in interferometric accuracy, but without the integer
fringe-order ambiguity of conventional single-wavelength interferometry.
For the illustrated embodiment the largest synthetic wavelength is 720
micrometers and the distance L is measured absolutely over a .+-.180
micrometer range about zero. When L is equal to zero there is no optical
path length difference between the reference and object beams in the
interferometer optics 18. For values of L outside this .+-.180 micrometer
range the measurement is relative, with an ambiguity interval of 360
micrometers. However, for many metrology applications there is sufficient
knowledge of the object under measurement to remove this ambiguity.
The synthetic wavelengths must be chosen so as to substantially eliminate a
possibility of introducing integer errors in Eq. (7) and Eq. (8). This
restraint places upper limits on the size of the synthetic wavelengths
used in the three-wavelength interferometer system 1. It can be shown that
the following conditions must be satisfied:
.LAMBDA..sub.12 <1/.DELTA.m(.LAMBDA..sub.13 /4-L/2(.DELTA..LAMBDA..sub.12
/.LAMBDA..sub.12 +.DELTA..LAMBDA..sub.13 /.LAMBDA..sub.13)) (9)
and
.LAMBDA..sub.13 <1/.DELTA.m(.lambda./4-L/2(.DELTA..lambda..sub.13
/.LAMBDA..sub.13 +.DELTA..LAMBDA./.lambda.))+.lambda.. (10)
where the uncertainties .DELTA.m, .DELTA..lambda., .DELTA..LAMBDA..sub.12,
and .DELTA..LAMBDA..sub.13 refer to the maximum absolute values of the
possible errors in any one of the parameters m, .lambda., .LAMBDA..sub.12,
and .LAMBDA..sub.13, respectively.
Referring to FIG. 2 there is shown a high-resolution displacement
measurement performed by the three-wavelength interferometer system 1 of
FIG. 1. The object was moved slowly towards the interferometer optics 18
by a piezoelectric translator mounted behind the object mirror. The
measurement repeatability was 0.5 nm.
Referring to FIG. 3 there is shown a profile of a central 1.times.1 cm
region of a 7.5 cm diameter, f/2 unsilvered parabolic mirror. Each one of
the 100 independent distance measurements made for this profile was
absolute. The three-color interferometer system of the invention is
particularly useful for profiling unusual topographical surfaces and
optical components that cannot be tested by conventional full-aperture
interferometry.
Since each of the 100 measurements was absolute, there was no requirement
to interpret fringes or perform high-bandwidth phase tracking as the
mirror was being translated from one point to the next. It should be noted
that the slope of 20 micrometers of profile variation per millimeter of
scan near the edge of the data grid is well beyond the capability of a
conventional full-aperture figure-testing interferometer. This capability
makes the three-wavelength interferometer system of the invention
particularly useful for figure metrology of unusual optical components,
such as off-axis aspheres and segmented optics. In general, the
profilometry accuracy is determined by the flatness of travel of the XY
stage, which must be characterized for high-precision measurements.
Alternatively, a Fizeau-teype geometry may be used for the interferometer
optics so that the measurement is less sensitive to random mechanical
motion of the stage.
Although the present invention has been described in the context of
specific wavelengths and optical components it should be realized that
other wavelengths and more or less than the number of optical components
shown in the figures may be employed, while yet obtaining the same result.
Also, although the various lens elements are depicted as simple lens
elements it should be realized that each may include a number of optical
components to achieve the desired function. Thus, while the present
invention has been particularly shown and described with respect to an
embodiment thereof, it will be understood by those skilled in the art that
changes in form and details may be made therein without departing from the
scope and spirit of the invention.
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