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Laser gage using chirped synthetic wavelength interferometry
Peter de Groot* and John McGarvey
The Boeing Company, P.O. Box 3999, Seattle, WA 98124
ABSTRACT
An absolute-ranging interferometer will be described that is suitable for dimensional gaging
and surface profiling in manufacturing applications.
The interferometer has a two-frequency
source and a continuously tuned or "chirped" synthetic wavelength. The fiber-coupled
experimental system uses an eye-safe 25µW, 0.25mm diameter collimated probe beam; and has
an absolute distance measurement accuracy of 3µm over a 150mm dynamic range.
1. INTRODUCTION
A number of optical technologies have been proposed to complement the proven mechanical
and electronic gaging methods already in use in the manufacturing environment.
The most
common types of optical gages are based on triangulation1 or equivalent geometric effects.
Several imaging systems based on intensity modulation laser radar have also been proposed,2
and impressive results have recently been obtained using white-light interferometry (coherence
radar) .3
Monochromatic laser interferometers are currently employed in manufacturing for highprecision displacement measurement and calibration. The Hewlett Packard Laser Gage and the
Zygo Axiom are two well-known examples of interferometric laser gages. However, a limitation
with these instruments relates to the interference phase ambiguity. Interferometry with a single,
constant wavelength cannot be used to measure a distance without ambiguity of one-half of one
wavelength. The beam cannot be broken and only highly-reflective "cooperative" targets such as
mirrors and retroreflectors can be used.
_____________________________
*
Present address: Zygo Corporation, Laurel Brook Road, Middlefield, CT 06455
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Absolute distance interferometers capable of measuring distances without phase ambiguity
would be very useful for gaging to rough surfaces, coordinate measurement and suface
profilometry.4 Concepts for laser-based absolute distance interferometers generally fall into two
classes, involving either multiple fixed wavelengths or continuously tunable sources.
Fixed-
wavelength methods are capable of very high accuracy, but a succession of measurements at
different wavelengths is required in order to remove all phase ambiguities.5,6
Frequency
modulation interferometers (FM laser radar) have no phase ambiguity but are limited in accuracy
by the tuning bandwidth.7,8
The laser gage described in this paper combines the advantages of both of these classes of
absolute-distance interferometer.
The combined spectrum of two laser sources is used to
generate a synthetic wavelength Λ; corresponding to the spatial beat-frequency of the fringe
contrast in the interferometer. The unusual feature of the present instrument is that the synthetic
wavelength is continuously tuned or "chirped" in a way that is analogous to FM laser radar. The
resulting chirped synthetic wavelength (CSW) interferometer can measure absolute distances with
a greater precision than FM interferometers, without resorting to the optical complexity of many
competitive synthetic-wavelength systems. Experimental results demonstrate the usefulness of
CSW interferometry for many dimensional gaging applications.
2. THEORY
The CSW principle can be understood by
Detector
considering the simple interferometer shown in
Figure 1. The detector measures an intensity that
varies periodically with the round-trip phase
velocity optical path difference
x
Source
between the
reference and object mirror paths. If the source is
Object
Mirror
not monochromatic, then the modulation depth of
the intensity variation will also depend on the
group-velocity path difference
= . The intensity
Reference
Mirror
function can be written
I = 1 + V ( Z ) ⋅ cos ( k x ) ,
(1)
Figure 1: Michelson interferometer with a
non-monochromatic source.
where
N is the average angular wavenumber of
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9 is the fringe contrast, and can be
calculated from the Fourier Transform of the spectral distribution M N of the source: 9
the source emission. The absolute value of the function
V (Z ) =
F {j ( k )}
(2)
∫ j(k ) dk
where
F {j ( k )}= ∫ j ( k )e
−ikZ
dk .
(3)
By choosing an appropriate spectral distribution it is possible to generate contrast functions that
are useful for metrology applications.
Suppose for example that the source
spectrum is composed of two lorentzian
1.2
α and separation β in
wavenumbers. The combined emissions
of two single-mode lasers would produce
such
a
spectrum
(Figure
2).
From
Equation (2) the contrast is
V =
e −α Z
2
1 + A ⋅ cos( φ) ,
0.8
0.6
α
0.4
0.2
0
79997
(4)
79999
80001
80003
WAVENUMBER ( cm^-1)
where
Figure 2: Example of the theoretical combined
φ = βZ ,
A=
β
1
RELATIVE POWER
lines of linewidth
(5)
optical spectrum of two lasers.
2 j1 j2
,
2
2
j1 + j2
(6)
and M and M are the relative strengths of the two lines. The range dependency of the contrast 9
when j = j is shown in Figure 3, for an example linewidth α =0.1cm-1 (500MHz) and
1
2
wavenumber separation
β =2cm-1 (10GHz). (These values were chosen because they make nice
theory graphs...other values are used in the experimental system.) The overall decline in contrast
is a consequence of the linewidth, and the quasi-periodic nature of the contrast is related to the
wavenumber separation. The synthetic wavelength
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Λ = 2π c / β
(7)
1
0.5 GHz LINEWIDTH
the contrast curve, and
FRINGE CONTRAST
is equal to the separation of the minima in
β may be thought of
as the synthetic wavenumber for the source.
In
order
measurement,
to
9
distance
must
somehow
we
determine the phase
function
perform
10 GHz SEPARATION
0.5
0
φ = Z β of the contrast
0
5
10
15
OPTICAL PATH DIFFERENCE (cm)
in Equation (4) without tracing
out a curve such as the one shown in Figure
3.
Since the phase is a function of the
synthetic wavenumber
distance
β as well as the
= , information about the fringe
Figure 3: Theoretical contrast curve for the twowavelength source spectrum shown in Figure 2.
contrast function can be obtained at a fixed
distance
by
varying
the
wavenumber
separation of the two lines in the source spectrum.10
wavenumber
In CSW interferometry, the synthetic
β is linearly chirped over a total amount γ during a period 7 :
β = ( t / T − 1 / 2) γ + β 0 .
(8)
The result is shown in Figure 4 for a
β 0 =30cm-1, γ =5cm-1 and the round-trip
path length
= =10cm.
The spacing
between the contrast minima is inversely
γ , and the time position of
the first minimum is related to β 0 . The
phase φ is now a time-dependent
proportional to
function that can be parameterized by a
frequency
time
1.2
FRINGE CONTRAST
j1 = j2 , α=0,
theoretical example where
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
TIME (sec)
I and a phase offset φ 0 at
t = 0:
φ = ( t / T − 1 / 2) f + φ 0 .
(9)
Figure 4: Theoretical variation in fringe contrast
while the wavenumber β is ramped from 27.5cm1 to 32.5cm-1 over a period 7 of 1 sec.
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These two parameters may be extracted from the contrast curve by any of the commonly known
means of frequency and phase estimation. Comparing Equations (8) and (9) it can be seen that
Z = 2π f / γ
(10)
Z = φ0 / β0 .
(11)
and
Since the group-velocity optical path length
= appears in both Equations (10) and (11), either one
of these equations could be used for range measurement.
The absolute distance is easily
obtained without phase ambiguity by measuring the frequency of the signal shown in Figure 4 and
∆Z / Z would be better with the
phase measurement and Equation (11), since in practice the wavenumber separation β 0 can be
made very much larger than the chirp range γ .
applying Equation (10). On the other hand, the relative precision
In CSW interferometry, both the frequency and the phase of the time-dependent contrast are
used together to determine absolute distance. The frequency is used to obtain a range estimate
2 πf / γ , which is then used to remove the 2 π ambiguity in the measured phase offset φ 0 .
These steps are summarized in the equation
  2πf φ0  φ0 
Z = Int 
− +
Λ .
γ
π
π
Λ
2
2




The function
(12)
Int{ } in Equation (12) returns the nearest integer to its argument, and introduces
the correct multiple of
2 π into the synthetic phase measurement. Thus by using both the
frequency and phase of a time-dependent fringe contrast function for a tunable two-wavelength
source, it is possible to combine the high accuracy of two-wavelength interferometry with the
simplicity and absolute ranging capabilities of chirp laser radar.
3. IMPLEMENTATION
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5
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In Figure 5 there is shown a schematic
of the experimental CSW laser gage that
we have assembled.
The source is
MODULATED
POWER SUPPLY
SIGNAL
PROCESSING
composed of two Sharp LTO80 modestabilized laser diodes, DC biased at
LASER 1
approximately 45mA for a power output of
2.5mW
per
wavenumber
diode.
The
DETECTOR
average
N is 8.05 × 10 −4 cm (780nm
wavelength)
and
the
wavenumber
-1
is 34.6cm
(165GHz),
separation β 0
LASER 2
ISOLATOR
corresponding to a synthetic wavelength
Λ of 2mm. A chirp range γ of 6.3cm-1
PZT
FIBER
OPTIC
FOLD
MIRROR
GRIN
(30GHz) is achieved by simultaneously
TARGET OBJECT
current tuning the laser diodes in opposite
directions
with
waveform.
a
5Hz,
The
3mA
current
triangle
modulation
superimposed on the DC bias introduces a
Figure
2mW variation in power output of each of
wavelength interferometer.
5:
Experimental
chirped
synthetic
the diodes; however, the power variations
are complementary and that the total
power output is constant.
Fiber Connector
As shown in Figure 5, the laser beams
BOEING
are combined by a prism and coupled into
a fiber.
Approximately 25µW of optical
Probe Beam
power is sent to the target. This power
level is class I at 780nm and may be
considered eye safe.
The interference
1 inch
signal is obtained by combining the light
scattered from the target surface with the
natural 4% Fresnel reflection from the end
of the fiber. The light returning through the
fiber is collected at the detector shown in
Figure 5. Approximately 0.5µW of the light
at the detector comes from the fiber end
Figure 6:
Fiber-coupled probe head for range
and depth measurements.
The 25µW output
beam is 250µm in diameter.
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reflection and about 1nW is normally
from
calibration is
the
target.
Continuous
MEASURED DISTANCE ( mm )
returned
provided by a separate
interferometer, not shown in figure 6, that
has a fixed optical path difference and
operates in parallel with the fiber probe.
The calibration interferometer compensates
for the frequency drift characteristic of laser
diodes. In order to create a signal that is
carrier
signal
oscillating
at
1.25kHz
with
150
125
100
75
50
75
100
125
150
175
200
STAGE ENCODER READING (mm)
is
generated by a piezo-electric transducer
(PZT)
175
50
proportional to the fringe contrast, an
interference-phase
200
an
amplitude of 1.5µm. The interference signal
is high-pass (linear phase) filtered with a
Figure 7: Distance as measured by the CSW
interferometer recorded as a function of the
position of a precision stage.
cutoff frequency of 500Hz, rectified and lowpass filtered with a cutoff of 1kHz to yield
the fringe-contrast curve. Data is acquired by a personal computer over a period of 100ms during
each of the positive and negative slopes of the triangle-wave modulation, and the frequency
and the phase
I
φ 0 are extracted by Fourier Analysis.
The instrument can be fitted with a fiber-coupled probe head for a variety of manufacturing
gage applications. An example probe for range and depth measurement is shown in Figure 6.
This probe is designed for use with non-cooperative (rough surface) targets, and uses a narrow,
250µm diameter, collimated beam for measuring through small holes and gaps. The small beam
size is obtained with a 0.15 pitch graded-index (GRIN) lens integrated into the fiber bulkhead
connector. The same probe can be used for simple profiling applications where the object is
translated perpendicularly with respect to the beam.
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The accuracy of the laser gage can be
by
comparing
distance
measurements to the optical encoder
readings on a precision translation stage.
In order to suppress speckle phenomena
for this test, the target is a mirror with an
ND2.0 filter to reduce the return beam
intensity.
The results of the accuracy
test are shown in Figure 7. A histogram
of the measurement error, here defined
NUMBER OF MEASUREMENTS
determined
40
35
100 MEASUREMENTS TOTAL
30
3 microns RMS
25
20
15
10
5
0
-20 -16 -12 -8
-4
0
4
8
12 16 20
MEASUREMENT ERROR (microns)
as the difference between the CSW
interferometer result and the optical
encoder reading for each point in the data
Figure 8: Histogram of measurement errors for
set, is shown in Figure 8.
the data shown in Figure 7. The bin size is 2µm
and the standard deviation is 3µm.
With the ND2.0 filter removed, the
interferometer is sensitive enough to
operate with non-specular targets, even
with an unfocused beam. The curve in Figure 9 is plot of the distance to the back side of a penny
as a function of scan position across the penny. The data has been post-processed according to
procedures described by Vry and Fercher to compensate for speckle effects.11,12 The expanded
profile in Figure 9 shows the 75µm columns in the Lincoln memorial relief. Figure 10 shows a
scan taken across a hole in a block of anodized aluminum. The cross-sectional plot reveals that
the hole has two diameters, with the smaller diameter beginning at about 200µm from the bottom
of the hole.
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4. ACKNOWLEDGMENTS
The
authors
are
pleased
to
acknowledge the contributions of Ron
70.00
Hagman, Randy Babbitt, Greg Garriss,
69.95
work.
RANGE (mm)
David Leep and Luis Figueroa to this
Jeff Lees provided invaluable
assistance in opto-mechanical design for
packaging
the
system,
and
Betsy
69.90
69.85
69.80
69.75
Richards wrote many of the original
69.70
computer programs for data acquisition.
0.0
5.0
10.0
15.0
20.0
25.0
SCAN POSITION (mm)
The CSW interferometer was developed
at the Boeing High Technology Center
with funding from the Boeing Commercial
Figure 9: Profile of the back side of a penny
Airplanes Group and the Boeing Defense
.
150
BEAM DIRECTION
125
RANGE (mm)
& Space Group.
100
75
50
SCAN DIRECTION
25
25
50
75
100
125
SCAN POSITION (mm)
Figure 10: Cross-section of a hole in a blackanodized aluminum block.
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2
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Vertatschitsch, "High-precision fiber-optic position sensing using diode laser radar techniques,"
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3
T. Dresel, G. Hausler and H. Venzke, "Three-dimensional sensing of rough surfaces by
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4
N. A. Massie and H. John Caulfield, "Absolute distance interferometry," Proc. SPIE 816, 149-
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5
C. W. Gillard and N. E. Buholz, "Progress in absolute distance interferometry," Opt. Eng.
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6
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8
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12
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