Phase-Shifting Interferometry Papers
|
|
Brad Kimbrough, James Millerd, James Wyant,
and John Hayes
Proceedings of SPIE Vol. 6292, page
62920F-1-12, 2006
An on-axis, vibration insensitive, polarization Fizeau interferometer is
realized through the use of a novel pixelated mask spatial carrier phase
shifting technique in conjunction with a low coherence source and a
polarization delay-line. In this arrangement, coherence is used to
effectively separate out the orthogonally polarized test and reference beam
components for interference. With both the test and the reference beams
on-axis, the common path cancellation advantages of the Fizeau
interferometer are maintained. The interferometer has the unique ability to
isolate and measure any surface that is substantially normal to the optical
axis of the cavity. Additionally, stray light interference is substantially
reduced due to the source’s short coherence. An expression for the fringe
visibility on-axis is derived and compared with that of a standard Fizeau.
Using a 15 mW source, the maximum camera shutter speed, used when measuring
a 4% reflector, was 150 usec, resulting in very robust vibration
insensitivity. We experimentally demonstrate the measurement of both sides
of a thin glass plate without the need to modify the plate between
measurements. Experimental results show the performance of this new
interferometer to be within the specifications of commercial phase shifting
interferometers. |
|
Robert M. Neal and James
C.
Wyant
APPLIED OPTICS, Vol. 45, page
3463, 20 May
2006
A new instrument, the polarization phase-shifting
point-diffraction interferometer, has been developed by use of a
birefringent pinhole plate. The interferometer uses polarization to
separate the test and reference beams, interfering what begin as orthogonal
polarization states. The instrument is compact, simple to align, and
vibration insensitive and can phase shift without moving parts or separate
reference optics. The theory of the interferometer is presented, along with
properties and fabrication techniques for the birefringent pinhole plate and
a new model used to determine the quality of the reference wavefront from
the pinhole as a function of pinhole size and test optic aberrations. The
performance of the interferometer is also presented, along with a detailed
error analysis and experimental results.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-45-15-3463 |
|
Matt Novak, James
Millerd, Neal
Brock, Michael
North-Morris, John
Hayes, and James
Wyant
APPLIED OPTICS, Vol. 44, page
6861, 10 November
2005
Recent technological
innovations have enabled
the development
of a new
class of dynamic
(vibration-insensitive) interferometer
based on a
CCD pixel-level
phase-shifting approach.
We present
theoretical and
experimental results for
an interferometer
based on this
pixelated phase-shifting
technique. Analyses
of component
errors and instrument
functionality are
presented. We show
that the majority
of error sources
cause relatively
small magnitude
peak-to-valley errors in
measurement of
the order of
0.002–0.005 . These
errors are
largely mitigated by
high-rate data
acquisition and
consequent data
averaging. URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-44-32-6861 |
|
Neal Brock, John Hayes, Brad Kimbrough, James Millerd, Michael
North-Morris, Matt Novak and James C. Wyant
Proceedings of SPIE Vol. 5875 (SPIE, Bellingham, WA), page
58750F-1, 2005
The largest limitation of phase-shifting interferometry for optical
testing is the sensitivity to the environment, both vibration and air
turbulence. In many situations the measurement accuracy is limited by the
environment and sometimes the environment is sufficiently bad that the
measurement cannot be performed. Recently there have been several advances
in dynamic interferometry techniques for reducing effects of vibration. This
talk will describe and compare two dynamic interferometry techniques;
simultaneous phase-shifting interferometry and a special form of spatial
carrier interferometry utilizing a micropolarizer phase-shifting array. |
|
James Millerd, Neal Brock, John Hayes, Brad Kimbrough, Matt Novak,
Michael North-Morris and James C. Wyant
Proceedings of SPIE Vol. 5856 (SPIE, Bellingham, WA), page
14, 2004
The measurement accuracy of an interferometric optical test is generally
limited by the environment. This paper discusses two single-shot
interferometric techniques for reducing the sensitivity of an optical test
to vibration; simultaneous phase-shifting interferometry and a special form
of spatial carrier interferometry utilizing a micropolarizer phase-shifting
array. In both techniques averaging can be used to reduce the effects of
turbulence and the normal double frequency errors generally associated with
phase-shifting interferometry. |
|
James E. Millerd, Stephen J. Martinek, Neal J. Brock, John B. Hayes and
James C. Wyant
Proceedings of SPIE Vol. 5380 (SPIE, Bellingham, WA), page
422, 2004
We demonstrate an instantaneous phase-shift, point diffraction
interferometer that achieves high accuracy and is capable of measuring a
single pulse of light at NA greater than 0.8. |
|
Babak N. Saif, James Millerd,
Ritva Keski-Kuha, Lee Feinberg, and J. C. Wyant
Proceedings of SPIE Vol. 5494 (SPIE, Bellingham, WA), page
152, 2004
Digital Speckle Pattern Interferometry (DSPI) is a well-established
method for the measurement of diffuse objects in
experimental mechanics. DSPIs are phase shifting interferometers.
Three or four bucket temporal phase shifting
algorithms are commonly used to provide phase shifting.
These algorithms are sensitive to vibrations and can not be
used to measure large optical structures far away from the
interferometer. In this research a
simultaneous phase shifted interferometer,
PhaseCam product of 4D Technology Corporation in Tucson Arizona, is modified
to be a Simultaneous phase shifted Digital Speckle
Pattern Interferometer (SDSPI). Repeatability,
dynamic range, and accuracy of the SDSPI are
characterized by measuring a 5 cm x 5 cm carbon fiber coupon. |
|
James E. Millerd, Neal J. Brock, John B. Hayes and James C. Wyant
Proceedings of SPIE Vol. 5531 (SPIE, Bellingham, WA), page
264, 2004
We demonstrate a phase-shifting, point diffraction interferometer that
achieves high accuracy and is capable of measuring
a single pulse of light. The measurement system utilizes a polarizing
point diffraction plate to generate a synthetic reference beam that is
orthogonally polarized to the transmitted test
beam. The plate has very high polarization contrast, works over an extremely
broad angular and spectral range, and is only 100 nanometers thick.
The unique features of the polarizing element make
the system amenable to measuring strongly convergent light from high
numerical aperture optics without the need to use a point reference
source to calibrate the system. Results of
measuring optics with numerical apertures as high as NA 0.8 are presented. |
|
James Millerd, Neal Brock, John Hayes, Michael North-Morris, Matt Novak
and James Wyant
Proceedings of SPIE Vol. 5531 (SPIE, Bellingham, WA), page
304, 2004
We demonstrate a new type of spatial phase-shifting, dynamic
interferometer that can acquire
phase-shifted interferograms in a single camera frame. The interferometer is
constructed with a
pixelated phase-mask aligned to a detector array. The phase-mask encodes a
high-frequency
spatial interference pattern on two collinear and orthogonally polarized
reference and test beams. The phase-difference
between the two beams can be calculated using conventional N-bucket
algorithms or by spatial convolution. The wide spectral response of
the mask and true common path
design permits operation with a wide variety of interferometer front
ends, and with virtually any light source
including white-light. |
|
James C. Wyant
Optics and Photonics News, Vol.
14, pages 36-41,
April 2003
|
|
Michael B. North-Morris, Jay VanDelden, and James C. Wyant
APPLIED OPTICS, Vol. 41, page
668, February
2002
We realized what we believe is a new phase-shifting scatterplate
interferometer by exploiting the polarization
characteristics of a birefringent scatterplate. The common-path design of
the interferometer reduces its sensitivity to
environmental effects, and phase shifting allows quick and accurate
quantitative measurements of the test surface. A major feature of the
birefringent scatterplate approach for phase
shifting is that no high-quality optical components are required in the test
setup. The theory of the interferometer is
presented, the procedure for the fabrication of the birefringent
scatterplate is described, and experimental
results are shown. URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-41-4-668 |
|
Conrad Wells and James C. Wyant
Proceedings of SPIE Vol. 3134 (SPIE, Bellingham, WA), page
466, 1997
An imaging ellipsometer has been developed which employs phase shifting
interferometry to characterize the ellipsometeric
parameters. A modified Michelson interferometer is used in conjunction with
a Wollaston prism to generate two interferograms
with orthogonal polarization states. Subtraction of the phases in the two
interferograms yields the ellipsometeric parameter
D. The fringe modulation of the two
interferograms is used to calculate the
ellipsometeric parameter Y.
The characterization of the average
intensity of the interferogram is the largest contributor
to the errors in the modulation. New algorithms for reducing the
errors in modulation calculations for phase shifting
interferometry are presented. The design of the instrument, results
of measurements and algorithms for modulation
characterization will be presented |
|
Conrad Wells and James C. Wyant
Proceedings of SPIE Vol. 3121 (SPIE, Bellingham, WA), page
13, 1997
An imaging ellipsometer has been developed which employs phase shifting
interferometry to characterize the ellipsometeric
parameters. Polarized light from a laser or incoherent source is collimated
and reflected off of the surface under test. A
modified Michelson interferometer is used in conjunction with a Wollaston
prism to generate two interferograms with
orthogonal polarization states. Subtraction of the phases in the two
interferograms yields the ellipsometeric parameter
D .The
fringe modulation of the two interferograms is used to calculate the
ellipsometeric parameter Y.
The instrument uses imaging optics to image
the surface under test to a CCD, yielding a truly two
dimensional ellipsometeric measurement. The design of the instrument
and results of measurements will be presented. |
|
Chiayu Ai and James C. Wyant
APPLIED OPTICS, Vol. 27, page
3039, 15 July
1988
The phase errors caused by spurious reflection in
Twyman-green and Fizeau interferometers are studied. A practical
algorithm effectively eliminating the error is presented. Two other
algorithms are reviewed, and the results obtained using the three algorithms
are compared. URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-27-14-3039 |
|
Chiayu Ai and James C. Wyant
APPLIED OPTICS, Vol. 26, page
1112, 15 March
1987
If the nonlinearity of the motion of a piezoelectric
transducer (PZT) can be described as a quadratic function, the integrated
intensity of one frame in phase shift interferometry can be calculated using
the Fresnel integral. For a PZT with smaller nonlinearity, the rms
phase error is almost linearly proportional to the quadratic coefficient.
The effects of PZT nonlinearity on the three- and four-bucket algorithms are
compared. URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-26-6-1112 |
|
Katherine Creath and James C. Wyant
Proceedings
of SPIE,
Vol. 645, page 101, 1986
Two-wavelength holography and phase-shifting
interferometry are combined to measure aspheric surface contours with
variable sensitivity. In this technique, the surface is effectively
tested at a synthesized longer equivalent wavelength leq=la
lb/Abs[la
- lb] using measurements made at
wavelengths la and
lb where the difference of the phases measured for
la and lb
yields modulo 2p phase at leq.
A mask of point apertures is placed over the detector array in order to
resolve closely spaced fringes. This technique has an rms
repeatability of leq/100. Limits
to this technique are discussed and results are shown. |
|
Gudmunn A. Slettemoen and James C.
Wyant
JOSA A, Vol. 3, page 210,
1986
The interference between a uniform reference wave and
a speckle object wave results in variable fringe contrast and background
level. Taking these variations into account, we optimize system
parameters of phase-shifting speckle interferometry. The results show
that the optimal reference intensity should always be equal to one fourth of
the detector's saturation level. The optimal reference to the
object-intensity shows an increase from one up to, in most practical cases,
six as a chosen interference dynamic range increases from its minimum value.
The dependence of a maximal fraction of acceptable measurements on the
dynamic range is calculated. Numerical examples indicate that we may
hope for a readout accuracy in the range of 1/50th to 1/100th of a fringe
period and still cover more than half of the image area with acceptable
data. These data are taken without spatial averaging and have maximum
resolution. URL:
http://www.opticsinfobase.org/abstract.cfm?URI=josaa-3-2-210 |
Katherine Creath, Yeou-Yen Cheng, and James C.
Wyant
Optica Acta, Vol. 32, page 1455, 1985
Two-wavelength holography and phase-shifting interferometry are combined to
measure the phase contours of deep wavefronts and surfaces, such as those produced by
aspherics, with a variable sensitivity. When interference fringes are very closely spaced,
the phase data contain high frequencies where 2p ambiguities
cannot be resolved. In this technique, the surface is tested at a synthesized longer
equivalent wavelength. The phase of the wavefront is calculated modulo 2p
using phase-shifting techniques at each of two visible wavelengths. The difference
between these two phase sets is the phase of the wavefront as it would be measured at leq =l1l2/|l1-l2|, assuming that 2p ambiguities can be removed at leq. This
technique enables surfaces to be contoured to an accuracy of leq/l00. |
|
Ming Chang, Ching-Piao Hu, Philip Lam and James C. Wyant
APPLIED OPTICS, Vol. 24, page 3780,
November 15, 1985
A digital phase shifting technique capable of
quantitatively determining the phase of holographic interferometric
displacement fringes is presented. This technique uses computer
control to take data and calculate surface deformation. The phase
value at each detector point can be calculated by taking four successive
intensity data frames with the reference phase shifted between each frame.
The displacement fringe order number can be assigned by adding or
subtracting 2p from a data pont until the phase
difference between adjacent data points is less than p.
Experimental results show that this technique can precisely determine a
fraction of a fringe with an accuracy of ±1o.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-24-22-3780 |
Yeou-Yen Cheng and James C. Wyant
APPLIED OPTICS, Vol. 24, page 3049, September 15, 1985
This paper describes some
practical methods to calibrate the phase shifter in phase-shifting interferometry (PSI).
The phase shifter used in the experiment is a piezoelectric transducer (PZT) that has a
nonlinearity of <l%. Using the quantitative method described in this paper, the
repeatability in the measurement of the phase-shifting angle is ˜9.046 deg rms, and
the 3s value is 0.139 deg. A calibration-insensitive phase
calculation algorithm is discussed and compared with other synchronous detection equations
(e.g., the three-bucket or the four-bucket method). Experimental results verify the
calibration-insensitive mechanism of the self-calibrating algorithm.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-24-18-3049 |
K. N. Prettyjohns, S. DeVore, Eustace Dereniak, and
J. C. Wyant
APPLIED OPTICS, Vol. 24, page 2211, July 15 1985
A direct phase measurement interferometer
designed and constructed to operate at a 3.8-µm wavelength is described. The
interferometer uses a deuterium fluoride laser as the light source, zinc selenide
transmitting optics, and a 32- X 64-element PtSi infrared CCD detector array with digital
processing electronics and a graphics display on a desktop microcomputer. The instrument,
which is useful for measuring a figure error caused by thickness variations in dielectric
coatings applied to infrared optics, gives a wave front measurement repeatability of <l/50 rms.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-24-14-2211 |
|
Yeou-Yen Cheng and James C. Wyant
APPLIED OPTICS, Vol. 24, page 804, March 15 1985
This paper describes a method to
enhance the capability of two-wavelength phase-shifting interferometry. By
introducing the phase data of a third wavelength, one can measure the phase of a very
steep wave front. Experiments have been performed using a linear detector array to
measure surface height of an off-axis parabola. For the wave front being measured
the optical path difference between adjacent detector pixels was as large as 3.3 waves.
After temporal averaging of five sets of data, the repeatability of the measurement is
better than 25-Å rms (l = 6328 Å).
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-24-6-804 |
|
Yeou-Yen Cheng and James C. Wyant
APPLIED OPTICS, Vol. 23, page
4539, 15 December 1984
This paper
describes a technique that combines ideas of phase
shifting interferometry (PSI) and two-wavelength interferometry (TWLI) to
extend the phase measurement range of conventional single-wavelength PSI.
To verify theoretical predictions, experiments have been performed using a
solid-state linear detector array to measure 1-D surface heights.
Problems associated with TWLPSI and the experimental setup are discussed.
To test the capability of the TWLPSI, a very fine fringe pattern was used to
illuminate 1024 element detector array. Without temporal averaging,
the repeatability of measuring a surface having a sag of ~100mm
is better than 25-Å (0.0025%) rms.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-23-24-4539 |
|
J. C. Wyant, B. F. Oreb, and
P. Hariharan
APPLIED OPTICS, Vol. 23, page
4020, 15 November 1984
Two-wavelength holography has been shown to be quite
useful for testing aspheric surfaces since it can produce interferograms
with a wide range of sensitivities. However, TWH has the drawback that
the accuracy attainable from measurements on photographs of the fringes is
limited. It is shown how this limitation can be overcome by using
electronic techniques to evaluate the phase distribution in the interference
pattern.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-23-22-4020 |
Self-referencing wavefront sensor (1220 KB)
K. Underwood, J.C. Wyant, and C.L. Koliopoulos
Proc. SPIE,
Vol. 351, 1983
A modified Smartt
point-diffraction interferometer employing phase-shifting electronic phase
measurement techniques is described. Special techniques making it
possible for the interferometer to give good visibility interference fringes
for a large range of input tilts are discussed. A trade-off between
acceptable values of wavefront tilt and light efficiency is presented. |
|
R. N. Shagam and J. C. Wyant
APPLIED OPTICS, Vol. 17, page 3034, October 1, 1978 |
|
J. C. Wyant
APPLIED OPTICS, Vol. 14, page 2622, November 1975
An analysis is performed to determine the accuracy with which an ac heterodyne lateral
shear interferometer can measure wavefront aberrations if a white light extended source is
used with the interferometer, and shot noise is the predominate noise source. The analysis
shows that for uniform circular or square sources larger than a derived minimum size, the
wavefront measurement accuracy depends only upon the radiance of the source and not upon
the angular subtense of the source. For a 1-msec integration time, a 25-cm2
collecting area, and a source radiance of 10 W/m2-sr the rms wavefront error is
approximately 1/30 wave, assuming the signal is shot noise limited. It is shown that for
both uniform circular and square sources an optimum shear distance is approximately 1/2
the aperture diameter required to resolve the light source. Comments are made on the
optimum shear for nonuniform radiance distributions.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-14-11-2622 |
J. F. Ebersole and J. C. Wyant
APPLIED OPTICS, Vol. 13, page 1904, May, 1974 |
|
J. C. Wyant
APPLIED OPTICS, Vol. 13, page 200, January 1974
A grating lateral shear interferometer
is described that can be used with a white light source. The use of the interferometer
with certain types of extended sources is also demonstrated.
URL:
http://www.opticsinfobase.org/abstract.cfm?URI=ao-13-1-200 |
