Indium tin oxide (ITO) thin films have been widely used in displays such as liquid crystal displays and touch panels because of their favorable electrical conductivity and optical transparency. The surface shape and thickness of ITO thin films must be precisely measured to improve their reliability and performance. Conventional measurement techniques take single point measurements and require expensive systems. In this paper, we measure the surface shape of an ITO thin film on top of a transparent plate using wavelength-tuning Fizeau interferometry. The surface shape was determined by compensating for the phase error introduced by optical interference from the thin film, which was calculated using the phase and amplitude distributions measured by wavelength-tuning. The proposed measurement method achieved noncontact, large-aperture, and precise measurements of transparent thin films. The surface shape of the sample was experimentally measured to an accuracy of 40 nm, mainly limited by the accuracy of the reference surface of 30 nm.
A new calibration method is proposed to separate the profile error caused by the sphericity of the scanning stylus in 3- dimensional contact profilometry. To reduce uncertainty in surface profile measurements, compensation of the stylus sphericity has become a critical issue. In optical flat testing, the three-flat method, which can separate the reference error from the measured deviations, is well known. Although there are also several methods of calibration of the stylus sphericity in contact profilometry, to extract the error precisely remains a challenge. Here we consider a new algorithm for this that uses four measurements including new combinations of the two styluses. The algorism yields four deviation data of the sum of the object profile and the stylus sphericity. With this method, we can extract the surface profile, while keeping the stylus error minimum.
We propose a synthesis of phase-shifting algorithms for Fizeau interferometry of high numerical-aperture spherical surfaces. Several approaches have been reported for spherical surface measurements such as phase shifting, carrier fringe, and wavelength tuning. The commonly used method of phase shifting with mechanical phase modulation suffers from spatial nonuniformity of the phase step within the observing aperture. We operated seven algorithms designed for different phase steps on the same set of interference fringes recorded in a one phase-shift sequence, and determined the object phase from each of the algorithms depending on the aperture position. The resultant phase distribution showed minimum systematic errors.
Internally scattered light in a Fizeau interferometer is generated from dust, defects, imperfect coating of the optical components, and multiple reflections inside the collimator lens. It produces additional noise fringes in the observed interference image and degrades the repeatability of the phase measurement. A method to reduce the phase measurement error is proposed, in which the test surface is mechanically translated between each phase measurement in addition to an ordinary phase shift of the reference surface. It is shown that a linear combination of several measured phases at different test surface positions can reduce the phase errors caused by the scattered light. The combination can also compensate for the nonuniformity of the phase shift that occurs in spherical tests. A symmetric sampling of the phase measurements can cancel the additional primary spherical aberrations that occur when the test surface is out of the null position of the confocal configuration.
A method to reduce the phase measurement errors generated from internal-reflection light noise in a Fizeau
interferometer is proposed. In addition to an ordinary phase-shift by a mechanical translation of the reference surface, the
test surface is also mechanically translated between each phase measurement to further modulate the signal phase. For
spherical tests, a mechanical phase-shift generally generates a spatial non-uniformity in the phase increment across the
observing aperture. It is shown that a minimum of three positional measurements is necessary to cancel out the
systematic error caused by this non-uniformity. Linear combinations of the three measured phases can also cancel the
additional primary spherical aberrations that occur when the test surface is out of the null position of the confocal
configuration.
For the surface shape measurement of a semiconductor with a highly reflective index, it is important to effectively
suppress the harmonic signals from multiple reflections. In application, the phase extraction algorithm should have a
maximum value when there is no phase-shift miscalibration. In this presentation, a new 4N - 3 phase extraction algorithm,
which has the ability to suppress harmonic signals and exhibits a fringe contrast maximum value when there is no phaseshift
error, was derived. This new 4N - 3 algorithm consists of a new polynomial window function and a discrete Fourier
transform term and has the ability to compensate for 2^{nd}-order nonlinearity in the phase shift. The suppression ability of the new polynomial window function is compared with other conventional window functions. The sampling functions of
the new 4N - 3 algorithm have much smaller amplitudes in the vicinity of the detection frequency than does synchronous
detection or other phase extraction algorithms with conventional window functions.
Interferometric surface measurement of parallel plates presents considerable technical difficulties owing to multiple beam interference. To apply the phase-shifting technique, it is necessary to use an optical-path-difference-dependent technique such as wavelength tuning that can separate interference signals in the frequency domain. In this research, the surface shape and optical thickness variation of a lithium niobate wafer for a solid Fabry-Perot etalon during the polishing process were measured simultaneously using a wavelength-tuning Fizeau interferometer with a novel phase shifting algorithm. The novel algorithm suppresses the multiple beam interference noise and has sidelobes with amplitudes of only 1% of that of the main peak. The wafer, which was in contact with a supporting glass parallel plate, generated six different interference fringes that overlapped on the detector. Wavelength-tuning interferometry was employed to separate the specific interference signals associated with the target different optical paths in the frequency domain. Experimental results indicated that the optical thickness variation of a circular crystal wafer 74 mm in diameter and 5-mm thick was measured with an uncertainty of 10 nm PV.
Nonlinearity and non-uniformity of phase-shifts significantly contribute to the error of the evaluated phase in phase-shifting interferometry. However, state of the art error-compensating algorithms can counteract the linear mis-calibration and first-order nonlinearity associated with the phase-shift. We describe an error expansion method that is utilized to construct a phase-shifting algorithm that can compensate the second-order nonlinearity and non-uniformity of phase-shifts. The conditions for eliminating the effect of second-order nonlinearity and non-uniformity of phase-shifts are given as a set of linear equations for the sampling amplitudes. We developed a novel 11-sample phase-shifting algorithm that can compensate for the second-order nonlinearity and non-uniformity of phase-shifts and is robust up to a 4^{th} harmonic. Experimental results show that the surface shape of a transparent plate could be measured with a precision of 1 nm, over the 120-mm-diameter aperture.
The interference fringe order of a transparent glass plate was determined using a three-surface wavelength-tuning Fizeau
interferometer and an excess fraction method. We employed multiple-surface interferometry considering the potential for
simultaneous measurement of the surface shape and geometric thickness. The optical thickness signal was separated
from the three interference signals in the frequency space. A frequency selective phase-shifting algorithm and a discrete
Fourier analysis detected the phase of the modulated interference fringes. The optical thickness obtained by wavelengthtuning
Fizeau interferometry is related to the group refractive index. In contrast, the optical thickness deviation obtained
by the phase-shifting technique is related to the ordinary refractive index. These two kinds of optical thicknesses were
synthesized with the help of the dispersion relation of a fused-silica glass. Finally, the interference fringe order was
determined using an excess fraction method that could eliminate the initial uncertainty of the refractive index.
Error estimation method of phase detection in phase shift method is proposed. Phase detection algorithms extract phase
of fringes from several interferograms that are acquired during phase shifting. The Fourier domain expression of phase
detection algorithms show frequency response for sine and cosine components, and it shows behavior of detected phase
in the case if phase shifting error exists. However, these two response functions do not directly show frequency response
of phase detection itself. On the contrary, newly proposed frequency response function directly shows frequency
response of phase detection. And it clearly shows the behavior of phase detection algorithm when phase tuning error
exists. The proposed method is inspired by the Bode plot. It is easy to assume that magnitude plot also can be defined in
addition to the phase plot. The magnitude plot can be used for prediction of the sensitivity to the signal and noise. And
the phase plot can be used for error estimation of phase detection in the presence of phase tuning error. After some
investigations, it was found that there is good agreement between the developed frequency response function and
calculated error value. Therefore, it can be used as an error estimation method for phase detection algorithm. A window
function modifies specifications of phase detection algorithm. Comparisons of several numbers of window functions on
phase detection method were demonstrated using proposed method. Additionally, we discuss window function, which
makes phase detection algorithm insensitive to phase detuning.
Absolute optical thickness is a fundamental parameter for the design of optical elements. In semiconductor industry,
it is necessary to measure the absolute optical thickness of the central part of the projection lenses with a high
accuracy. However, even when the geometrical thickness is perfectly known, a typical refractive index of fused-silica
has an ambiguity of 6 × 10^{-5} that gives an uncertainty of 180 nm in the optical thickness for a 3 mm-thick plate.
Moreover, the optical thickness measured by white light interferometry and wavelength tuning interferometry is an
optical thickness with respect to not the ordinary refractive index but the group refractive index. We measured the
ordinary optical thickness of a fused silica plate of 6-inch square and 3 mm thickness by a wavelength tuning
interferometer with a tunable phase shifting technique. We assumed the typical refractive index and dispersion of
the fused silica as approximate values. The absolute interference order for the optical thickness was finally
estimated, which gives a measurement resolution of typically 10 nm for the optical thickness.
In this report, error estimation method of phase detection in phase shift method is proposed. Phase detection algorithm
extracts phase of modulated signal from several numbers of interferogram that acquired during phase shifting. The
fourier domain expression of phase detection algorithms show frequency response for sine and cosine components. And
it shows behavior for phase detection in the case that phase shifting error exists. However, these two response functions,
those are response function for sine component and that for cosine component, do not directly show frequency response
of phase detection itself. On the contrary, newly developed frequency response function, which is derived from these two
frequency response function, directly shows frequency response of phase detection. And it clearly shows the behavior of
phase detection algorithm when phase tuning error exists. The newly developed frequency response function is similar to
the Bode plot. The magnitude plot shows sensitivity for frequency components. And the phase plot can be used for error
estimation of phase detection. There is good agreement between the developed frequency response function and
calculated error value. These results of comparison between error estimation using developed frequency response
function and calculated error value are shown in this report.
The surface flatness and the uniformity in thickness and refractive index of a mask-blank glass have been
requested in semiconductor industry. The absolute optical thickness of a mask-blank glass of seven-inch square
and 3mm thickness was measured by three-surface interferometry in a wavelength tuning Fizeau interferometer.
Wavelength-tuning interferometry can separate in frequency space the three interference signals of the surface
shape and the optical thickness. The wavelength of a tunable laser diode source was scanned linearly from 632
nm to 642 nm and a CCD detector recorded two thousand interference images. The number of phase variation of
the interference fringes during the wavelength scanning was counted by a temporal discrete Fourier transform.
The initial and final phases of the interferograms before and after the scanning were measured by a phase
shifting technique with fine tunings of the wavelengths at 632 nm and 642 nm. The optical thickness defined by
the group refractive index at the central wavelength of 337 nm can be measured by this technique. Experimental
results show that the cross talk in multiple-surface interferometry caused a systematic error of 2.0 microns in the
measured optical thickness.
Profiling of optical surfaces with discontinuous steps by monochromatic interferometry has the ambiguity of multiples of a quarter wavelength. Wavelength-tuning interferometry can measure these surfaces with a unit of synthetic wavelength that is usually much larger than that of the original source. In order to solve this problem, the fractional phases of the interferograms before and after wavelength tuning should be carefully estimated. Phase-shifting interferometry with a mechanical phase shift by a PZT transducer determines the fractional phases of the interferograms with a resolution of better than one part in 250 of the wavelength. After subtracting the mechanical drift of the test surface during wavelength tuning, the absolute distance between the test surface and the reference surface is measured with an uncertainty better than a quarter wavelength. An optical flat with two gauge blocks 1 mm in height contacting the surface is measured by a Fizeau interferometer. Experimental results demonstrate that the surface profile can finally be measured with an accuracy of 20 nm.
Wavelength tuning interferometry can distinguish interference signals from different surfaces in frequency space. The optical thickness variation of each layer of a multiple-surface object was measured by a new tunable phase measuring algorithm which can efficiently compensate for the frequency detuning of the interference signals. A two-layer object consisting of Lithium Niobate (LNB) wafer on the supporting glass parallel was measured by the new tunable algorithm in a Fizeau interferometer. Experimental results show that the optical thickness variation of the top wafer was measured with an error of λPV over a 70 mm diameter aperture.
Wavelength scanned interferometry can distinguish in frequency space interference signals from different surfaces , and therefore allows the measurement of optical thickness variation between several quasi-parallel surfaces of a composite transparent object. Discrete Fourier analysis of the signal spectrum with a suitable sampling window can then detect the phase of the individual signals. The actual frequencies of the various signals can deviate from their nominal detection frequencies because of refractive index dispersion of the material and/or nonlinearities in the wavelength scanning. This creates problems for conventional sampling window functions, such as the von Hann window, because they are sensitive to detuning of the signal frequency. Therefore we have derived an error-compensating algorithm (with 2N-1 samples and individual phase steps of 2p/N) with a modified triangular window that allows some frequency detuning and can determine the phase of any specific harmonic order within the frequency range of the detected signal. A composite object consisting of four reflecting surfaces was measured using the new algorithm in a Fizeau interferometer. Experimental results show that the new algorithm measured the front surface and the optical thickness variations in a glass-air-glass cavity with an error of 10 nm rms over a 90 mm diameter aperture.
Wavelength-scanning interferometry allows the simultaneous measurement of the surface profile and the optical thickness variation of a parallel plate. Previously we have derived two error-compensating algorithms for the detection of the fundamental and third harmonic frequencies. This requires a certain fixed ratio of the interferometer's air gap width to the optical thickness of the parallel plate. As the test plate becomes thinner, so does the air gap of the interferometer, and the wavelength-tuning range eventually becomes insufficient to give the necessary phase shift. By swapping the detection frequencies of the two algorithms, the phase-shift step can be augmented threefold compared with the previous interval. The resultant scheme allows a three-times larger air gap and hence requires only one third of the wavelength-tuning range compared with the previous scheme. Measurements of a BK7 plate of 1 mm thickness and a ZnSe plate of 5 mm thickness in a Fizeau interferometer showed residual errors caused by nonlinear wavelength-scanning and higher order multiple-reflections.
Interferometric measurement of the refractive index inhomogeneity of a glass parallel plate has been demonstrated experimentally to a resolution of 10^{-6}. Wavelength scanning interferometry allows the simultaneous measurement of optical thickness and surface shape of a parallel optical plate. A new sampling function suppresses the first-order refractive index dispersion and multiple-beam interference noise to give a measurement resolution of 2 nm in optical thickness.
Wavelength scanning interferometry allows the simultaneous measurement of the surface profile and the optical thickness variation of a parallel plate. However, it is necessary to evaluate the modulation frequencies of the signal and noise which depend on the optical thickness and dispersion of the test plate. New nineteen-sample, wavelength scanning algorithms allow variation in these parameters and give a measurement resolution of 1-2 nanometers rms. Measurement of a BK7 near-parallel plate of 250 mm diameter and 25 mm thickness was demonstrated in a Fizeau interferometer.
Non-destructive profiling of the front and rear surfaces of a transparent media by optical interferometry is described. Interferometric measurement of a transparent parallel media leads to problems of multiple-beam interference noise between the two surfaces. A wavelength scanning interferometer with new sampling functions can determine both surface shapes simultaneously suppressing internal reflection noises less than order of R^{2}(lambda) where R is the reflection index of the media and (lambda) is the source wavelength.
Japanese Ultimate Flatness Interferometer (FUJI) is a Fizeau type flatness interferometer that is capable of measuring flatness over 310 mm diameter. The concept and technologies applied to FUJI are explained. To demonstrate the performance of FUJI, an international comparison was held with Australia, and the difference of two independent measurements were smaller than four nanometers.
In a phase-shifting interferometer, spatial non-uniformity of the phase modulation happens in such a case where an aspherical mirror is compared to the corresponding aspherical standard surface which is translated along the optical axis by a piezo electric transducer. The amount of phase shift is different from position to position across the observing aperture depending on the direction cosine of the testing surface. In another case, when the reference optical flat is translated by two or more piezo-electric transducers, we cannot ensure that the reference surface moves strictly parallel to the optical axis. When these transducers have different sensitivities, the phase modulation is not longer spatially uniform and varies across the observing aperture.
In phase shifting interferometers, spatial non-uniformity of the phase modulation often happens in such cases where as aspherical (or spherical) mirror is compared to the corresponding aspherical standard surface which is translated along the optical axis by piezo electric transducer to introduce phase modulation. The amount of phase shift is then different across the observing aperture depending on the gradient of the testing surface. The nonlinear sensitivity of the phase modulator causes a significant errors in measured phase when there is a spatial nonuniformity in phase shift. Many phase measuring algorithms reported to date cannot compensate for the spatial nonuniformity if there is a nonlinear phase shift. It is shown that if we add a new symmetry to the sampling functions of the phase measuring algorithm we can suppress the phase errors caused by the spatial non-uniformity of the phase shift. The new algorithms need at least one more image frame to acquire the symmetry. The lowest-order algorithm compensating for quadratic spatially non-uniform phase modulation consists of six frames.
In phase shifting interferometers, spatial non-uniformity of the phase modulation often happens and affects high- precision phase measurement. Many phase measuring algorithms have been reported which compensate for nonlinear sensitivities of the phase shifter. This nonlinearity of the phase shifter usually gives only a constant bias to the measured phase in these algorithms. However, when the phase shift is spatially nonuniform, the measured phase is shown to suffer significant errors from these bias phase. We have shown that if we add a new symmetry to an algorithm we can remove the errors caused by the spatial nonuniformity of the phase shift. The algorithm needs at least one more image frame to acquire the symmetry. The lowest-order algorithm that compensates for a quadratic and spatially nonuniform phase shift consists of six frames. We have compared the performance of the new algorithm on several types of phase nonuniformity to the conventional error-compensating algorithms.
In phase shifting interferometry, many error-compensating algorithms have been reported. Such algorithms suppress systematic errors caused by nonlinear sensitivities of the phase shifter and nonsinusoidal waveforms of the signal. However, in a Fizeau interferometer where both error sources are equally dominant, the most common group of the algorithms produces errors comparable to those produced by discrete Fourier algorithms which have no capability to compensate for phase-shift errors. It is shown that if an algorithm has an extended immunity to nonlinear phase shift, it can suppress the effects of both error sources simultaneously and yield much smaller errors. When a phase-shifting algorithm is designed to compensate for the systematic phase-shift errors, it becomes more susceptible to random noise. The susceptibility of phase shifting algorithms to random noise is analyzed with respect to their immunity to phase-shift errors. It is shown that for the most common algorithms for nonlinear phase shift, random errors increase as the number of samples becomes large. This class of algorithms has an optimum number of samples for minimizing the random errors, which is not observed in the Fourier algorithms. However, for the new algorithms with an extended immunity to nonlinear phase shift, random errors decrease as the number of samples increases.
In phase-shifting interferometry, nonlinear motion of the phase shifter and non-sinusoidal waveform of the signal are the two most common sources of systematic errors in the measured phase. A j + 4-sample algorithm is derived which compensates for quadratic nonlinearity of the phase shifter and the effect of harmonic components of the signal up to the jth order. The susceptibility of the algorithm to random noise is also discussed.
Elastic scattering of light reflects an inhomogeneous interface between two media. Applied to surfaces the technique is sensitive to roughness levels in the sub-Angstrom region. This makes it an excellent tool for studying minute changes in the surface structure while processing materials. Examples are given of real-time total integrated scattering applied to stress analysis of metallization films and monitoring of thermal stability of silicides.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print format on
SPIE.org.