18-Tutorial 3a

Kathy Sheehan

Informations

• Publié par: Anjyo
• Nombre de lectures: 39
• Langue: English

Extrait

BY ROBERT SMYTHE,
ZYGO CORP.
forMEASURE
MEASURE
Instantaneous phase-
measuring interferometry
provides production-level provel
metrology.
hase-measuring interferometry (PMI) is the metrolo- PMI—to measure these phase differences. The classic PMI
gy tool of choice for the optical industry, measuring technique, phase-shifting interferometry (PSI), uses multi-Pkey parameters such as surface figure, transmitted ple frames of data acquired in sequence while shifting the
wavefront, homogeneity, and radius of curvature for process phase. Phase shifting is performed through either mechan-
control and quality assurance. Previously confined to the ically changing the length of the interferometer cavity or
quality-control laboratory, PMI has become necessary tech- by changing the wavelength during data acquisition such
nology for monitoring surface figure and transmitted wave- as wavelength specific PSI (WSPSI). Both PSI approaches
front on the production floor. Manufacturing tolerances for provide very low measurement uncertainty.
optical components as diverse as cell phone lenses and large Recently, new techniques have been invented for
telescope mirrors require interferometric-level metrology in enhanced performance: Fourier-transform PSI, for measur-
environments in which low-noise testing facilities are ing multiple surfaces, and IPMI, for data acquisition in pro-
1impractical. New instantaneous PMI (IPMI) techniques duction environments. We are going to focus on the latter.
can operate in these production environments with success, In all PSI techniques, each pixel independently extracts
but care must be taken regarding systematic errors to assure the wavefront phase using the measured intensity variation
good metrology. as a function of phase shift. The measured intensity I
depends on phase ϕ via the equation
The Basics
An interferometer measures the phase difference between I = A + B cos ϕ (1)
two wavefronts. To measure an optical component, a refer-
ence surface is compared to the test part, where each com- where A and B are the offset and amplitude of the
ponent produces a separate wavefront. Modern interfer- observed intensity variation. Since A, B, and ϕ are
ometers use computerized data acquisition techniques— unknowns, we require at least three independent intensity
34| SPIE’s oemagazine |November/December 2004|
ILLUSTRATION BY RANDALL NELSONmeasurements to recover the phase; typically, more are The most common calibration technique is measuring a
taken. In all PSI techniques, each pixel independently high-quality calibration part. We assume the calibration
extracts the phase information. part has very small wavefront errors compared to the
For optimal performance, it is important that the optical interferometer. The measured result should therefore
rays trace back over the same paths in the reference surface reveal only the systematic errors in the interferometer.
and test parts. This is true in the most common Fizeau PSI This calibration measurement is saved and subtracted
interferometers. The higher the quality of the test part and from future test part measurements.
the better the fringe alignment, the lower the measurement National standards institutes can measure calibration
uncertainty. Optical rays tracing back over the same paths parts to very low uncertainties. Once the calibration part
negate imperfections in the optical system, even if the wave- leaves the calibration lab, however, numerous factors can
front within the system has measurable errors. This is not degrade its usefulness. If a part was calibrated under tight
true with all PMI techniques or interferometer configura- laboratory conditions (typically 20°C ± 0.1K), the meas-
tions. This natural alignment reduces measurement uncer- urement only applies in an equal environment. This is espe-
tainties in high-end commercial Fizeau interferometer sys- cially true for parts mounted in metal housings—differen-
tems to much better than λ/300. With proper temperature tial thermal expansion warps the part when the measure-
control, reference surface calibration, and careful handling of ment temperature deviates from the test temperature, and
the test part—the kinds
of conditions afforded in
test laboratories—such
commercial systems can
achieve measurement
uncertainties of better
than λ/1000.
IPMI systems sacrifice
this natural alignment
to obtain rapid phase
data. The key innova-
tion in IPMI is captur-
Large-amplitude vibration can introduce greater error into measurements taken with a PMI systeming the interferometer
(left) than with an IPMI system (right), which captures data instantly.phase data in a single
camera frame to freeze
out vibration and turbulence effects. To get around the thermal cycling will cause thermal gradients through the
multiple measurement requirements inherent in equation 1, test part, also warping the calibration part.
IPMI encodes the intensity variation spatially rather than The actual gradients will depend on the interferometer
temporally, using either hardware or software techniques. temperature, the air temperature, the amount of space
To spatially encode the intensity variation, hardware between the test part and the reference, and the tempera-
techniques apply specialized optical elements to replicate ture cycling period of the production environment. It is
phase-shifted images, and simultaneously display the not unusual for production or even large laboratories to
images on the same or multiple cameras. Software tech- exhibit thermal cycles of ±0.5°C over various periods. This
niques leverage a constant phase shift across a single image magnitude of variation could cause uncertainties of 100
with a tilted interferometer wavefront, and mathematically nm in a 300-mm flat, or λ/6 uncertainty. Because the cal-
2extract the phase variation across the field. An advantage of ibration part is affected by the production-environment
the latter technique is an easy upgrade for existing PSI inter- temperature instabilities and measurement uncertainties
ferometer systems. Note that the optical
rays trace back over different paths so that
imperfections in the optical system are
not negated but measured; we call these
ray-mapping errors.
Calibration
All IPMI systems have separated optical
paths, which increases measurement
uncertainty. Uncalibrated system specifi-
cations of commercial IPMI instruments
range from λ/10 to λ/20, 15 to 30 times
worse than a PSI system. Some applica-
tions require system calibration to mini-
mize these large systematic errors.
|November/December 2004| SPIE’s oemagazine |35during calibration, this calibration process, though simple, tions induced in the measurement cavity. This data is
has limitations. stored, just like in the calibration part method and removed
The hardware IPMI approaches may be limited to the from future carrier fringe data sets. The system is internally
calibration part method, but the software-based carrier- calibrated off the gold-standard PMI system without
fringe IPMI technique has several other calibration reliance on external measurement artifacts. Both techniques
options. Carrier-fringe IPMI requires the introduction of are good to λ/50 uncertainties, sufficient for most produc-
significant tilt in the measurement cavity. The interferom- tion requirements.
eter contributes an increasing systematic error with increas-
ing cavity tilt because of ray-mapping errors, as noted After Calibration
above. Tilt-induced ray-mapping errors are, however, well With the interferometer calibrated, the remaining systemat-
understood, mathematically well behaved, and therefore ic errors are introduced by the reference surface, environ-
3,4easily calibrated and removed from the results. Before ment, and test part. The interferometer reference surface
calibration, these errors are typically less than λ/20, small and test part experience the same influences, primarily due
by IPMI standards but significant enough to require to temperature effects and mounting stresses. The smaller
removal from the data via calibration. the temperature variation, the better the measurement. Your
Extensive calibration processes that were previously con- measurement uncertainty is never better than the total
sidered impractical are now straightforward with today’s range of the measured variations. Quantifying the magni-
computers. Ray-mapping errors introduce non-axially-sym- tude of these variations establishes the best-case systematic
metric aberrations, typically coma and astigmatism. The errors in the test setup. The best method for accomplishing
first calibration technique leverages the mathematical this involves acquiring data over a long period, typically
smoothness of the aberrations. After acquisition of a series over several days at different times. The variations are pri-
of IPMI measurements with increasing tilt, we can calculate marily due to temperature changes.
and remove ray-mapping errors from the series. This tech- The remaining environmental influences of turbulence
nique is good to λ/50 and requires no special hardware or and vibration are primarily random in nature. Averaging
outside calibration. results minimizes these effects. In general, the random noise
The second technique uses the gold-standard PSI data decreases as the inverse square root of the number of aver-
acquisition to measure the non-axiall