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Description  |
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TECHNICAL FIELD
This invention relates generally to the measurement of roughness of optical
surfaces, and pertains more particularly to heterodyne profilometry for
measuring surface roughness.
DESCRIPTION OF THE PRIOR ART
The state of the art in measuring surface roughness of optical surfaces was
discussed by J. M. Bennett and J. M. Dancy in an article entitled "Stylus
Profiling Instrument for Measuring Statistical Properties of Smooth
Optical Surfaces", Applied Optics, Vol. 20, No. 10, pp. 1785-1802 (May 15,
1981). Techniques involving mechanical contact between a stylus and the
surface whose roughness is to be measured are ordinarily very sensitive to
changes in surface roughness. However, a surface contact technique imposes
extremely high local pressures on the surface under investigation, and
thus tends to disturb or deform the surface.
A non-contact optical heterodyne technique for measuring the surface
roughness of an optically reflective surface was described by G. E.
Sommargren in an article entitled "Optical Heterodyne Profilometry",
Applied Optics, Vol. 20, No. 4, pp. 610-618 (Feb. 15, 1981). According to
Sommargren's technique, two orthogonally polarized optical beams of
slightly different frequency are focussed as two separated focal spots on
the surface whose roughness is to be measured. One focal spot serves as a
reference, while the other focal spot scans the surface in a circular
pattern. The two beams are reflected by the surface so as to interfere
with each other. The intensity of the resulting interference pattern
varies sinusoidally with the different optical phase of the two beams,
which is proportional to the height difference between the two separated
focal spots on the reflective surface. This height difference, and hence
the differential optical phase, provides a measurement of surface
roughness. A heterodyne interferometer is used to measure the differential
optical phase, and hence to measure the surface roughness. However,
vibrational motion of the reflective surface distorts the differential
optical phase of the two reflected beams, and therefore renders the
surface roughness measurement unreliable.
SUMMARY OF THE INVENTION
It is an object of the present invention to measure roughness of an
optically reflective surface by means of an optical heterodyne
interferometric technique that is substantially insensitive to optical
phase jitter induced by vibrational motion of the reflective surface.
In accordance with the present invention, two laser beams of different
frequencies are focussed as concentric spots (one spot being larger than
the other) on a reflective surface whose roughness is to be measured. The
smaller spot has a maximum dimension smaller than any significant
deviation of the profile of the surface from spatial uniformity (i.e.,
absolute smoothness), and the larger spot has a minimum dimension larger
than any significant deviation of the surface profile from spatial
uniformity. The two beams are reflected from the surface, and the phase
difference between the two reflected beams is measured by heterodyne
interferometry. Because of the common path of the two reflected beams, the
phase difference measurement is substantially insensitive to vibration of
the reflective surface.
An optical heterodyne profilometer in accordance with the present invention
can be made using conventional components that are commercially available
at the present time, and is capable of resolving the optical phase
difference (within an accuracy of 0.01 degrees i.e., a sensitivity range
of 0.1 Angstrom) between two laser beams of different frequency reflected
along a common path from a surface whose roughness is to be measured.
Furthermore, an optical heterodyne profilometer according to the present
invention made with commercially available components can enable rapid
scanning (i.e., scanning at a rate in excess of 200 microns per second) of
the reflective surface under a focussed spot size of less than 2 microns
diameter for the smaller of the two concentric spots.
A preferred embodiment of the present invention is illustrated in the
accompanying drawing and described hereinafter in the specification of the
best mode presently contemplated for carrying out the invention.
DESCRIPTION OF THE DRAWING
FIG. 1 is a schematic representation of an optical heterodyne profilometer
in accordance with the present invention.
FIG. 2 is a schematic view of the portion of FIG. 1 showing concentric
first and second laser beams of different frequencies incident upon and
reflected from the surface whose roughness is to be measured.
BEST MODE OF CARRYING OUT THE INVENTION
In the embodiment of the present invention as shown in FIG. 1, a sample 10
having a reflective surface whose roughness is to be measured is
positioned on a translation stage 11, which is movable relative to a
stationary optical heterodyne profilometer 12. A translation controller
13, which is operable either manually or by means of an electrical
feed-back input from a focussing-monitor of the profilometer 12, controls
the movement of the translation stage 11 and hence of the sample 10
relative to the profilometer 12. Alternatively, the sample 10 could be
held stationary, and the profilometer 12 could be mounted for movement
relative to the sample 10.
The profilometer 12 comprises a laser 20, which emits a monochromatic beam
of visible electromagnetic radiation with an angular frequency
.omega..sub.o. The output from the laser 20 is polarized by a polarizing
beam splitter 21, and the resulting polarized beam is input to an
acousto-optical modulator (i.e., a Bragg cell) 22. As shown in FIG. 1, the
direction of polarization of the beam generated by the laser 20 is on the
plane of the paper, as indicated in the conventional manner by a pair of
arrows perpendicular to the beam path.
An oscillator 23 drives the Bragg cell 22 with an angular offset frequency
.omega..sub.a, which causes the Bragg cell 22 to emit a first beam with
the angular frequency .omega..sub.o and a second beam with a combined
angular frequency (.omega..sub.o +.omega..sub.a). In the preferred
embodiment, the laser 20 is an HeNe laser with an output of 0.5 mW at a
wavelength of 633 nm (i.e., an angular frequency of 475 THz). A typical
offset angular frequency is 30 MHz. Typically, the first and second beams
emitted by the Bragg cell 22 both have a diameter of about 1 mm.
The first beam with angular frequency .omega..sub.o is reflected from a
mirror 24 through a beam expander 25 to a beam splitter 26. The second
beam with angular frequency (.omega..sub.o +.omega..sub.a) is reflected
from mirrors 27 and 28 in sequence through a beam reducer 29 to the beam
splitter 26. The beam expander 25 comprises optical elements configured
and arranged so as to expand the diameter of the first beam, typically to
a diameter of about 25 mm. The beam reducer 29 comprises optical elements
configured and arranged so as to reduce the diameter of the second beam,
typically to a diameter less than 1 mm.
The beam splitter 26 reflects a portion of the expanded first beam and
transmits a portion of the reduced second beam to a photodiode 30, which
generates an electronic output signal R.sub.optical that serves as an
optical reference. Careful alignment of the first and second beams by the
beam splitter 26 so as to be collinear with each other enables the
photodiode 30 to produce maximum photocurrent output at frequency
.omega..sub.a.
The beam splitter 26 likewise transmits another portion of the expanded
first beam and reflects another portion of the reduced second beam to a
focussing lens 31, which focusses these other portions of the first and
second beams as first and second spots, respectively, on the surface of
the sample 10. The focussing action of the lens 31 causes the first spot
to be considerably smaller than the second spot, as illustrated in detail
in FIG. 2.
The first spot produced by the focussing of the expanded first beam has a
diameter that is smaller than any significant deviation from spatial
uniformity that would be likely to be present on the surface of the sample
10. The second spot produced by the focussing of the reduced second beam
has a diameter that is larger than any significant deviation from spatial
uniformity (i.e., absolute smoothness) that would be likely to be present
on the surface of the sample 10. Typically, the smaller first spot has a
diameter on the order of 2 microns, and the larger second spot has a
diameter on the order of 50 microns. The focussing lens 31 could be, e.g.,
a 50 mm, F/0.95 camera lens. Because the first and second beams are
incident upon the surface of the sample 10 along a common optical path,
the resulting first and second spots of illumination on the surface of the
sample 10 are concentric.
A quarter-wave plate 32 is interposed between the focussing lens 31 and the
reflective surface of the sample 10. The first and second beams are
reflected by the surface of the sample 10 back along a common optical path
through the quarter wave plate 32 and through the focussing lens 31 to the
beam splitter 26. The double passing of each of the first and second beams
through the quarter-wave plate 32 causes the direction of polarization of
the beams returning to the beam splitter 26 after having been reflected
from the surface of the sample 10 to be rotated 90.degree. from the
direction of polarization of the beams leaving the beam splitter 26 before
passing through the quarter-wave plate 32 on the way to the surface of the
sample 10.
As illustrated schematically in FIG. 2, the beam with angular frequency
.omega..sub.o, i.e., the expanded first beam, is reflected from the
surface of the sample 10 through an inverted cone of radiation having a
diameter of 25 mm at the focussing lens 31. The beam with angular
frequency (.omega..sub.o +.omega..sub.a), i.e., the reduced second beam,
is reflected from the surface of the sample 10 through an inverted cone of
radiation having a diameter of 1 mm at the focussing lens 31. The two
reflected beams concentrically overlap each other at the focusing lens 31,
and are propagated along a common path back to the beam splitter 26.
A portion of each of the common-path first and second beams reflected from
the surface of the sample 10 is reflected by the beam splitter 26 through
the beam reducer 29 to the mirror 28, and thence to a polarizing beam
splitter 33 interposed in the optical path between the mirrors 28 and 27.
The polarizing beam splitter 33 reflects a portion of each of these
reflected portions of the first and second beams to a photodiode 34 with a
direction of polarization that is orthogonal to the direction of
polarization of the beam from the laser 20, as indicated in the
conventional manner in FIG. 1 by a a pair of dots on the optical path.
The photodiode 34 generates an electronic output signal S, which is
proportional to the optical interference of the first and second beams
reflected along their common path from the surface of the sample 10. The
optical interference of the first and second beams reflected from the
surface of the sample 10 to the photodiode 34 has a beat frequency
.omega..sub.a, which in combination with the phase difference between the
interfering first and second beams provides a measure of the phase
difference between the reflected first and second beams.
In the process of measuring the surface roughness of the sample 10 (i.e.,
in the "surface profiling" process), the sample 10 is translated relative
to the common path of the first and second beams incident upon the
reflective surface. The concentric first and second beams thereby scan the
reflective surface so that the concentric first and second spots sweep
over the reflective surface. The sample 10 could be, e.g., a mirror for
use in a high-precision optical system. The surface of the mirror would
initially be polished to a generally uniform degree of smoothness by a
conventional polishing technique, and the optical heterodyne profilometer
12 of the present invention would be used to measure the degree of
smoothness achieved by the polishing technique.
The diameter of the first spot formed on the surface of the sample 10 is
too small to span completely any protuberance or indentation that amounts
to a substantial change from spatial uniformity on the surface. Thus, the
area of the first spot is too small to illuminate an entire protuberance
or indentation of significant size on the surface. However, the area of
the second spot formed on the surface of the sample 10 is large enough so
that the distribution of protuberances and indentations (i.e., the number
of deviations from spatial uniformity per unit area) illuminated by the
second spot remains substantially constant as the concentric first and
second spots are swept over the surface.
In being reflected from the surface of the sample 10, the first beam
travels to the photodiode 34 through a distance that varies with the
profile of the reflective surface as the concentric first and second beams
scan the reflective surface. Since the first beam illuminates the
reflective surface with the first spot, which is smaller than any
protuberance or indentation of significant size on the reflective surface,
the distance travelled by a wavefront of the first beam in being reflected
from the surface to the photodiode 34 is longer when the first spot is
formed on a depression or indentation on the surface, and shorter when the
first spot is formed on a bulge or protuberance on the surface. On the
other hand, since the second beam illuminates the reflective surface with
the second spot, which is larger than any individual protuberances or
indentations on the surface, the average distance travelled by all
portions of a wavefront of the second beam in being reflected from the
reflective surface to the photodiode 34 is substantially constant as the
first and second beams scan the reflective surface. Therefore, variations
in the phase difference between wavefronts of the first and second beams
reaching the photodiode 34 correspond to variations in the height or
profile of the reflective surface.
The phase difference measurement indicated by the output signal S of the
photodiode 34 is the difference between the phases of the concentric first
and the second beams reflected along their common path from the surface of
the sample 10. The reflected first beam provides an optical phase that is
precisely sensitive to deviations from spatial uniformity (i.e., precisely
sensitive to roughness) occurring on the surface of the sample 10. The
reflected second beam provides a reference phase with which the phase of
the reflected first beam is continuously compared. The two beams reflected
from the surface of the sample 10 have different frequencies and phases,
and therefore interfere with each other with a beat frequency that carries
the differential phase. This differential phase, which is measured by the
optical heterodyne profilometer 12, provides a measure of the roughness of
the reflective surface of the sample 10.
Referring to FIG. 1, another portion of each of the first and second beams
is reflected from the surface of the sample 10 via the beam splitter 26,
the beam expander 25, the mirror 24 and the Bragg cell 22 to the
polarizing beam splitter 21. A portion of each of these reflected
common-path first and second beam portions is reflected by the polarizing
beam splitter 21 to a focussing monitor 35, which indicates the quality of
the focussing of the first and second beams upon the reflective surface of
the sample 10. The best focussing occurs when the intensity of the beams
received on the focussing monitor 35 is maximum.
In a particular application, the intensity of the beams received on the
focussing monitor 35 could be measured visually. Any adjustment of the
position of the translation stage 11 that might be necessary to obtain
optimum focussing could be accomplished manually. Alternatively, however,
the focussing monitor 35 could comprise a photodetector for generating an
output signal proportional to the combined intensities of the first and
second beams incident upon the reflective surface of the sample 10, and
the translation controller 13 could be driven by that output signal so as
to move the sample 10 to the position of optimum focal quality.
The oscillator 23 also provides an electronic output signal
R.sub.electronic that serves as an electronic reference. The signals
R.sub.optical, S and R.sub.electronic are input to a signal processor 40,
which computes the differential phase between the two common-path first
and second beams reflected from the surface of the sample 10. The
differential phase measurement is linearly proportional to the degree of
surface roughness of the sample 10. Since any vibration of the sample 10
would impart substantially the same optical phase change to each of the
first and second beams, the differential optical phase computed by the
signal processor 40 is substantially unaffected by vibration of the sample
10.
The output of the signal processor 40 can be displayed on an oscilloscope
41. A Tektronix 7854 programmable oscilloscope has been found suitable for
displaying a root-mean-square (rms) reading, and a Tektronix 7834 storage
oscilloscope has been found suitable for phase variation comparisons.
For a theoretical understanding of the mode of operation of the optical
heterodyne profilometer 12, consider the electric fields E.sub.1 and
E.sub.2 of the first and second beams, respectively, reflected from the
surface of the sample 10. These two electric fields can be expressed as
waveforms.
E.sub.1 =.sqroot.2 F cos {.omega..sub.o t+.phi..sub.o (t)+.phi..sub.s
(t)}(1)
E.sub.2 =.sqroot.2 G sin {.omega..sub.o t+.phi..sub.a t+.phi..sub.o
(t)+.phi..sub.s (t)+.phi..sub.a (t)} (2)
where .sqroot.2 F and .sqroot.2 G are the amplitudes of the respective
waveforms, .phi..sub.o (t) is the common optical phase due to vibration of
the sample 10, .phi..sub.s (t) is the optical phase due to surface
roughness of the sample 10, .phi..sub.s (t) is the optical phase due to
surface roughness averaged over the larger second focussed spot, and
.phi..sub.a is the electronic phase associated with the offset frequency
.omega.hd a.
For a conventional "square-law" photodiode receiving light from two
different beams the integrity of the photodiode output is proportional to
the square of the electric fields of the two beams, i.e., I=E.sub.1
.multidot.E.sub.2. Multiplying equations (1) and (2) yields
I=FG sin {.omega..sub.a t+.phi..sub.s (t)-.phi..sub.s (t)+.phi..sub.a }+FG
sin {2.omega..sub.o t+.omega..sub.a t+2.phi..sub.o (t)+.phi..sub.s
(t)+.phi..sub.s (t)+.phi..sub.a }. (3)
Defining AC=FG sin {.omega..sub.a t+.phi..sub.s (t)-.phi..sub.s
(t)+.phi..sub.a }, and DC=FG, (since the photodiode responds to the
amplitude and not to twice the optical frequency), equation (3) becomes
I=AC+DC, (4)
where AC represents the alternating current response of the photodiode, and
DC represents the direct current response of the photodiode. the ratio
AC/DC is
AC/DC=sin {.omega..sub.a t+.phi..sub.s (t)-.phi..sub.s (t)+.phi..sub.a }.
(5)
In equation (5), the common optical phase .phi..sub.o (t) due to vibration
of the sample 10 has been eliminated. Thus, the surface roughness
represented by .phi..sub.s (t)-.phi..sub.s (t) can be measured despite any
vibration that the reflective surface of the sample 10 may be undergoing.
Also, the amplitude terms F and G have been eliminated in equation (5).
Thus, the resultant phase measurement is insensitive to any variations in
signal intensity that might occur. This technique for eliminating
dependence upon signal intensity is known as the electronic common-mode
rejection technique.
In equation (5), the calibration of optical phase .phi..sub.s
(t)-.phi..sub.s (t) can be simulated by using the electronic phase
.phi..sub.a. Since the electronic phase .phi..sub.a changes by 2.pi. when
the propagation length changes by 10 meters in free space for a 30 MHz
electromagnetic wave, an electronic phase change of 0.01.degree. can be
achieved by introducing a change of 0.3 mm in the length of a variable air
line 42 interposed between the oscillator 23 and the signal processor 40.
A particular embodiment has been described herein for an optical heterodyne
profilometer in accordance with the present invention. However, other
embodiments suitable for particular applications would become apparent to
workers skilled in the art upon perusal of the foregoing specification and
accompanying drawing. The description presented herein is illustrative of
the invention, which is more generally defined by the following claims and
their equivalents.
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