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Dynamic measurements using a Fizeau interferometer
Daniel M. Sykora and Michael L. Holmes
Zygo Corporation, 21 Laurel Brook Road, Middlefield, CT, USA 06455
ABSTRACT
Single-camera frame instantaneous interferometry is an alternative optical test method where environmental noise
prohibits conventional phase shifting methods. For the most demanding applications, the instrument should have high
light efficiency and sufficient source power to accommodate short camera shutter times, effectively freezing object
motion. Here we report on a new instantaneous Fizeau-type interferometer with fully coherent optics that provide high
light-efficiency and increasing lateral resolution with zoom, and a novel 4mW, stabilized 633 nm laser source for singleshot metrology with exposures as short as 12 microseconds. We illustrate how this instantaneous measurement
capability enables continuous live display of surface profiles and Zernike fits, and dynamic data acquisition for recording
varying surface profiles or cavity disturbances at a rate of 82 Hz.
Keywords: Instantaneous interferometry, dynamic measurements, live phase, stabilized HeNe laser.
1. INTRODUCTION
Metrology of optical components in severe vibration and turbulent environments presents a significant challenge to
interferometric methods. Single-frame or instantaneous interferometers obviate errors in phase recovery algorithms by
capturing all the necessary phase-shifted data in a single camera frame. Instantaneous interferometers collect
simultaneous phase shifts by encoding and detecting reference and measurement beams in such a way as to enable
manipulation of their relative phase.
The encoding process for instantaneous interferometry may be accomplished through spatial separation of the interfering
beams,1,2,3,4 through the introduction of a tilt angle, as is possible in a modified Fizeau,5,6,7 or through coherence
matching of two interferometers that operate in tandem.8,9 Simultaneous detection of three or more phase-shifted
intensity signals for every pixel in the field of view is then required for data reduction. This can be realized through
duplicate images, adjacent to each other on the same camera or directed to multiple cameras, usually phase shifted by
polarization.1,2,10 Full-sensor single camera architectures mitigate the critical alignment and signal balancing required of
simultaneous multi-image detection by employing localized spatial phase shifting, either by pixelated polarizer camera
mask11,12 or by introduction of carrier fringes.3,13 We prefer the carrier fringe acquisition to simplify the design, optimize
efficiency, and avoid limitations related to birefringence in polarization-based approaches.14,15
In this paper, we present a design that enables high-performance dynamic measurements using the carrier fringe method
on an optimized Fizeau interferometer platform. A systems approach satisfies the requirements of single frame
acquisition together with the high shutter speed needed to maximize interference contrast in the most severe
environments. The new design provides for high-speed dynamic measurements while maintaining traditional
performance requirements of wavefront fidelity and spatial resolution. Typical retrace errors associated with introducing
tilt between the reference and measurement beams are greatly reduced through careful optimization of the optical design,
and the calibration and correction of any remaining errors are well understood and implemented through efficient in situ
techniques utilizing the component or surface under test.
2. 633 NM LASER SOURCE
A high power laser source clearly improves acquisition speed and is a design requirement for high-speed dynamic
interferometry. Wavelength, coherence length, beam quality, and intensity stability must all be considered when
choosing a light source for an instantaneous Fizeau-type interferometer. Here we propose that a wavelength/intensitystabilized HeNe laser is the preferred light source for the widest range of industry requirements for optical component
and system test specifications.
Optical Measurement Systems for Industrial Inspection VII, edited by Peter H. Lehmann,
Wolfgang Osten, Kay Gastinger, Proc. of SPIE Vol. 8082, 80821R · © 2011 SPIE
CCC code: 0277-786X/11/$18 · doi: 10.1117/12.890853
Proc. of SPIE Vol. 8082 80821R-1
Dynamic metrology based on instantaneous single-frame exposure time requires a higher energy light source to reach
comparable camera signal-to-noise levels as phase-scanning techniques, where interferograms are sampled over longer
exposure times and multiple frames. The higher optical power requirements point to a solid state laser; however, this
choice is ruled out by the temporal coherence required to maintain contrast over test cavities that can be longer than 30
meters. High coherence is a difficult requirement to meet cost effectively at visible wavelengths, but is fully satisfied by
the HeNe laser which can have a coherence length of several hundred meters.
A further consideration is wavelength. Surface metrology places no fundamental requirement on the interfering
wavelength, but compatibility with legacy test standards and capital equipment forces a wavelength choice at 633 nm.
Although 633 nm is not well centered in the visible band, the HeNe laser was the earliest reasonably priced coherent
light source. Over the past several decades the optics industry has standardized many measurement processes and
accumulated a huge inventory of test equipment, transmission spheres, and other accessories designed specifically for
use at 633 nm.
If we accept that a high-powered HeNe laser is the ideal solution, there are technical hurdles in traditional HeNe design
that have traditionally left commercial HeNe lasers underpowered. An unstabilized HeNe laser exhibits small
wavelength variations and 2 or more modes under the gain curve as the laser tube equilibrates to the operating
environment; see Figure 1. While the variation in wavelength has no impact on most measurements, the constantly
changing modes in the laser contribute to occasional loss of contrast at certain cavity lengths and as much as 60%
variability of the laser intensity.
We elected to integrate an internally manufactured HeNe laser, with a proven track record in lithographic stage
metrology and expected running lifetime in excess of 100,000 hours, in order to simultaneously satisfy the power,
coherence and wavelength requirements for dynamic metrology. Our laser uses a longer tube for greater gain, together
with custom end-mirror coatings, end-mirror shapes, and gas fill. As Figure 1 illustrates, the decreased mode-spacing of
the higher power tube requires mode stabilization to reliably prevent three simultaneous modes and the corresponding
reduction in coherence length. Stabilization is achieved through a control loop that actively servos the length of the laser
to achieve both mode-locked wavelength (i.e., no loss of contrast in certain long cavities) and constant output power
independent of ambient temperature conditions. In normal operation in an interferometer, just one mode is selected for
output by means of a polarizer.
A further benefit of frequency stabilization is a more consistent power level. The output power distribution between the
lasing modes of an unstabilized HeNe laser are sensitive to ambient temperature excursions of the environment in which
the interferometer is being used. This is not the case with a stabilized HeNe laser in which the temperature of the laser
tube is actively controlled as part of the frequency stabilization servo. The experimental data of Figure 2 demonstrate
significant differences in power stability (for a selected polarization) between an unstabilized commercial 2 mW HeNe
laser and the stabilized HeNe with exposure to even small ambient temperature variations of 2 degrees Celsius.
Figure 1. HeNe laser gain curves for a typical 2 mW commercial laser and a high-power 4 mW laser illustrating
possible mode spacing (free-spectral-range) and polarization. Operation in a 3-mode state is indicated by the solid
lines, and operation in a 2-mode state is shown as dashed lines. Frequency stabilization is needed to reliably
suppress the 3-mode state for the 4 mW laser.
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Figure 2. Power Stability of a selected polarization for an unstabilized 2-mW commercial laser and our stabilized
4-mW laser. Variation in light intensity is shown versus ambient temperature variation over 17 hours.
As a final benefit cited here, a stable/predictable wavelength is useful in those applications sensitive to wavelength, such
as the design of refractive null correctors and computer generated holograms (CGH) for use with the interferometer. In
this case, a priori knowledge of expected wavelength and its variation between different interferometer mainframes is
required.
3. LIGHT EFFICIENT DESIGN
Perhaps the most critical system design parameter for dynamic metrology, beyond the fundamental encoding and
detection technique, is the light efficiency. As electronic shutter times decrease to a few hundred microseconds and
below, the challenge becomes insuring that the detecting camera(s) have sufficient illumination to yield high signal-tonoise ratios (SNR) in the acquired modulating interferogram(s). Figure 3 provides a block diagram of six major
component groups that influence light efficiency in a typical Fizeau interferometer: 1) the light source; 2) fold mirrors;
3) polarization creating, splitting, and maintaining optics; 4) illumination optics; 5) imaging optics; and 6) the camera.
Section 2 reviewed the 4 mW HeNe laser chosen as the high-power light source in our design. Applied system design
principles for the remaining five component groups are briefly discussed in the paragraphs that follow.
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Figure 3. Block diagram of the primary component groups that influence light efficiency in a typical Fizeau
interferometer. Polarization optics and fold mirrors are drawn to represent an influence across illumination and
imaging optics.
Mirrors are often added at the opto-mechanical design phase to fold an optical system into a targeted packaging
envelope. Choice of mirror design and placement can be one of the largest sources of light loss. A common choice for
fold mirror coatings is protected aluminum due to cost and typical surface quality, yet at 633 nm a single reflection will
lose > 15% of the incident light. If we assume three fold mirrors of 85% reflectivity across the optical system this will
lead to an accumulated loss of > 38%. Moving to higher reflectivity mirrors will minimize losses upon reflection. A
folded design will generally include a polarizing beam splitter to separate illumination and imaging paths. Failure to
maintain polarization purity will increase light loss in transmission or reflection through a polarizing splitter beyond the
typical 10%.
Illumination optics influence light efficiency of the overall system by defining the illumination beam numerical aperture
( NA) that is ultimately imaged at the detector, i.e. the collimated test beam diameter. Choice of the illumination NA is a
balance between the irradiance profile across the raw source beam (Gaussian for a HeNe laser) and the intensity drop-off
from center to edge deemed acceptable in the interferogram image. A flat intensity profile is the ideal for constant SNR
across the entire aperture, but this remains an elusive target without either giving up additional light (i.e. increasing the
NA and truncating more light) or disrupting the necessary spatial coherence of the beam with beam shaping optics.
Light efficiency in the center of the imaged aperture can be restricted primarily to anti-reflection (AR) coating
efficiencies on the optics and is readily controlled to an accumulated loss of < 5%.
Light efficiency in the imaging system is a choice between incoherent imaging (where the interferogram is imaged onto a
rotating diffuser disc, for instance, with the scattered light collected and relayed to the camera through finite conjugate
imaging) or coherent imaging (where the interferogram is imaged directly onto the camera sensor). Coherent imaging is
the clear choice where light efficiency is paramount since losses can be restricted to < 5% with laser-line AR coatings.
In contrast, an incoherent imaging system will show losses exceeding 50% due to backward and forward scattering from
the diffuser combined with light loss at vignetting apertures in the imaging lens(es).
Finally, selection of a scientific camera and the quantum efficiency of the chosen sensor will affect overall light
efficiency of the system. Commercial interline progressive-scan CCDs are known to range from 25% - 50% in quantum
efficiency. This, of course, must be balanced against sensor dimensions, resolution, frame rate, charge capacity, and read
noise in the selection of a camera.
Figure 4 displays acquired interferograms at exposure extremes in both a 4% reflecting cavity and a 90% reflecting
cavity that validate our systems approach to design. The overall system light efficiency enables exposures from 100
microseconds down to 12 microseconds while still suitably filling the camera detector wells for high SNR.
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Figure 4. Acquired interferograms demonstrating light efficient instrument design yielding full camera wells at
fringe peaks for bare glass and high-reflector cavities at 1200x1200 and 600x600 camera resolutions.
4. DYNAMIC MEASUREMENTS AWAY FROM NULL
Optics with diameters greater than 0.5 meters generally benefit from dynamic metrology due to separated metrology test
platforms; this is especially so with long-radius curved surfaces. Precision optics of this size can also be challenging to
fabricate due to a mismatch in tool and aperture sizes. The large surface area may require the use of sub-aperture
polishing tools along with an iterative procedure of polishing, testing, and correcting. In this scheme a larger percentage
of the diameter is resolved with each polishing run, and the number of iterations required for correction will decrease
with an interferometer capable of large slope acceptance and measurement accuracy away from interferogram null
conditions. Lower uncertainty in the presence of high slope enables a more accurate deterministic “hit map” and
improves convergence to desired figure. It is with this in mind that the nominal optical imaging of the interferometer
was optimized to limit rigid-body retrace uncertainty to less than 0.1 waves when measuring surface slopes beyond 70
nm / pixel at all zoom magnifications.
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Figure 5. Residual low-order peak-to-valley retrace uncertainty versus surface slope departure on surface under
test - presented with surface slope departure in units of nm/pixel and mrad.
Empirical validation of retrace uncertainty in the presence of large slope is provided in Figure 5 for three fixed
magnifications. Data reduction involved subtracting a synthetic null data set (i.e., nominal carrier fringe tilt) with in situ
calibration from data that sampled slope departure away from carrier fringe tilt. This difference map was then fit to 16
Zernike terms to capture the low-order retrace magnitude across the aperture when measuring in the presence of large
slope departure for all three fixed magnification coherent zooms. Results of Figure 5 show retrace uncertainty to be less
than 0.1 waves (or λ/10) at 1X and 1.7X zooms with surface slope departure up to 80 nm/pixel. In a real application one
might wonder how to relate all of this to an actual measurement. Figure 6 provides an example of an actual
measurement approaching 14 microns (22 λ) of peak-to-valley figure error with maximum surface slope departure of
0.58 mrad. With reference back to Figure 5, this equates to < 0.032 microns (0.05 λ) of uncalibrated retrace uncertainty
even in a cavity with significant deviation from null.
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Figuure 6. Wavefron
nt error approachhing 14 microns peak-to-valleyy and 0.58 mradd slope departurre resolved and
meaasured with our dynamic
d
interferoometer. A synthhetic fringe map and resulting phhase map are shoown.
5. LIVE DIISPLAY OF
F PHASE
One of the unnique capabilitties of an instaantaneous interrferometer is thhe potential to display a live unwrapped phhase map
in place of or
o beside the more
m
familiar raw
r
images off interferogram
m fringes. Muulti-frame tempporal phase alggorithms
simply cannoot duplicate th
his feature. The
T ability to both visually and programm
matically monnitor a live phaase map
transforms an
a interferometter into a morre intuitive meetrology tool capable
c
of greeatly simplifyinng otherwise complex
c
may be
tasks. It alsso allows a usser to visualize how the surrrounding enviironment and//or mounting configurations
c
influencing a measurementt at the level off nanometers. Dynamic surfface figure testiing and optical system alignm
ment are
offered below
w as two exam
mples where a live phase mapp enhances onne’s ability to efficiently
e
sam
mple data and make
m
the
necessary adjjustments to prrovide improveed metrology.
5.1 Dynamiic surface figu
ure testing
An instantanneous interferrometer, with sufficient peerformance, presents
p
certaiin advantagess over a mullti-frame
interferometeer even for classic surface figgure measurem
ments of spherees, flats, or otheer surface form
ms. When testiing parts
with high aspect ratios (diiameter vs. thicckness) it is often
o
difficult to
t mount partss without distoorting the figurre of the
surface undeer measuremen
nt. Self-centerring holders, or
o other comm
mon chucks, coommonly emplloy three-pointt contact
separated byy 120 degrees; without propeer care one caan imprint signnificant power,, astigmatism, and/or trefoil into the
surface figurre as seen in the example of Figure 7a. While thesee differences may
m be measuured with mullti-frame
interferometrry, it can often
n be a non-intuuitive and iterative process requiring
r
skill and knowledgge to reduce mounting
m
stresses. Wiith live display
y of unwrappeed phase, an operator
o
can monitor
m
how eaach adjustmentt in clamping pressure
affects mounnting stresses and decisionss on the nextt adjustment are
a based on real-time feeddback aiding even an
inexperienced operator. When
W
the figuree measuremennt stabilizes thiis becomes a clear
c
indicationn that one can proceed
confidently with
w a final measurement not influenced by how a part maay have been mounted.
m
Proc. of SPIE Vol. 8082 80821R-7
(a)
(b)
Figure 7. Two examples of dynamic surface profiling: a) a high aspect ratio (diameter/thickness) mounted with
and without clamping stress; and b) a 1/20th-wave cavity measurement dominated by slow moving turbulence.
A second benefit of measuring surface figure with an instantaneous interferometer is the ability to measure in the
presence of extreme turbulence by freezing and averaging out local phase disturbances in each individual frame; this can
be especially critical in long cavities. Figure 7b demonstrates how disruptive turbulence can be when trying to measure
a 1/20th-wave cavity. With the benefit of an instantaneous interferometer, a well known strategy for averaging out the
effects of turbulence is to actually introduce fast moving homogenized turbulence across the cavity with large fans. Any
vibrations introduced by this process are of little concern when acquisition can be shuttered to below 100 microseconds.
5.2 Optical system alignment and Zernike monitoring
Live display of wavefront error introduces new possibilities in the area of optical system alignment while monitoring
real-time Zernike feedback. A snapshot of such a live window is presented in Figure 8, and shows a full resolution
phase map with selected Zernike aberration coefficients and bar graph display. Optical systems with two or more
components may have many waves of misalignment in the resulting wavefront upon initial setup. Historically, when
using an interferometer to achieve final wavefront alignment a technician has iterated between rough align (for gross
adjustments) and interferogram views (for fine adjustments) and then used phase acquisition of the current state for
analysis of residual alignment errors to determine the next step. A carefully defined procedure is normally required to
allow larger adjustments and speed an otherwise tedious process. It is proposed here that using a live display of phase
for such an alignment process can not only make the adjustments more intuitive and deterministic, but will allow for
continuous adjustments and more rapid convergence to final alignment.
Optical systems including complex lenses, folded mirror systems, and optical nulls are challenging to align to
transmitted wavefronts of < 0.25 waves. Through the use of the industry standard interferogram file format (*.INT)
there exists an opportunity for synergy between metrology and ray-tracing software.16 Imagine measuring an optical
system and feeding the as-built wavefront into ray-tracing software for analysis, optimization, and recommendation on
compensating adjustments, then exporting the improved wavefront as a reference file. By subtracting this reference file
from the live phase map real-time Zernike feedback provides deterministic monitoring of the recommended adjustments
while working to a phase null that achieves the prescribed performance.
Proc. of SPIE Vol. 8082 80821R-8
Figuure 8. A snapsho
ot of a live phase data window aiding
a
the in proocess alignment of an optical syystem, currently
withh unmet tolerance thresholds on astigmatism
a
andd coma, terms 4 and
a 7 respectively.
6. DYNAM
MIC RECORDING
Another uniqque capability
y of an instanntaneous interfferometer is thhe potential too acquire, plaayback, and annalyze a
sequence of dynamic even
nts, or said anoother way, to record
r
the veryy disturbances that prevent more
m
traditionaal multiframe temporal phase algorrithms. Dynam
mic recording enables
e
a preciise collection of
o camera fram
mes for post-proocessing
into phase maps
m
that capturre events at speeeds up to and including the camera
c
frame rate
r (82 Hz forr our interferom
meter).
While the ennd result of dyn
namic recordinng may resembble a live displlay of phase, the
t details an operator
o
must consider
during measuurement set up
p are fundamenntally different.. Here the focuus is on acquissition rate, num
mber of frames,, manual
or external trigger,
t
data prrocessing, playyback rate, annd plotting feaatures/setup. Acquisition
A
ratte is perhaps the
t most
critical param
meter and shou
uld be determinned by the typee of event one is
i capturing to minimize the number
n
of fram
mes (i.e.,
memory) reqquired to accurrately capture an event. Forr example, vibbration and moodal analyses generally
g
requuire rates
greater than 10 frames/sec, while analyses of turbulencee effects are reaadily captured at rates near 1 frame/sec. Loong term
thermal channges due to amb
bient temperatuure changes may
m be acquiredd at intervals off minutes. Figgure 9 demonsttrates the
recording of an open flamee placed inside an interfering cavity as an illlustrative exam
mple. A digitall trigger input provides
p
o be initializedd by an externaal event intended to provide an
a acoustic or mechanical im
mpulse to
the option foor acquisition to
the surface or
o system underr test. In the case of reproduucible transientt events one cann imagine com
mbining multiplle image
sequences recorded varying
g trigger delayss to increase thhe effective tem
mporal samplinng rate.
…
Figuure 9. Playback of a three-dimennsional movie capturing the phaase disturbance of an open flam
me placed inside
an innterfering cavity
y.
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7. SUMMARY AND CONCLUSION
We have presented design principles and empirical validation of a high-power, high-efficiency Fizeau-type
instantaneous interferometer capable of single-frame exposures approaching 10 microseconds with maximized signal-tonoise ratio. The limiting birefringence errors associated with interferometers employing polarization encoding and
detection is avoided by use of a dense spatial carrier fringe technique combined with a new coherent optical design.
Residual measurement errors < 0.1 waves were presented for surface slope departure exceeding 70 nm/pixel. The
capability to freeze dynamic events with high refresh rate enables live display of phase with real-time monitoring of
Zernike coefficients which is used for dynamic surface profiling and live optical system alignment. Another option is
the recording of dynamic events with up to 82 Hz sampling. The new functionalities highlighted above result from the
rigorous optimization of light-efficiency, the development of a custom frequency-stabilized high-power laser and a
coherent optical system optimized for carrier-based acquisition. Such advances in instrument design greatly extend the
application space of laser Fizeau interferometers.
The authors gratefully acknowledge contributions from Peter de Groot, Xavier Colonna De Lega, John Filhaber, Jim
Soobitsky, Garth Gangaway, Richard Bills, Dave Bourque, Ken Jezek, Al Delp, Andrew Wirger, Jeremy Wise, and
Thomas Dresel.
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