High-speed noncontact profiler based on scanning white-light interferometry

We describe a system for fast three-dimensional profilometry, of both optically smooth and optically rough surfaces, based on scanning white-light techniques. The system utilizes an efficient algorithm to extract and save only the region of interference, substantially reducing both the acquisition and the analysis times. Rough and discontinuous surfaces can be profiled without the phase-ambiguity problems associated with conventional phase-shifting techniques. The system measures steps to 100 μm, scans a 10μLm range in 5 s, and has a smooth surface repeatability of 0.5 nm.     

Single-shot two-dimensional surface measurement based on spectrally resolved white-light interferometry

By analyzing the spectral domain's phase information, one can use spectrally resolved white-light interferometry (SRWLI) to obtain the profile with a single frame of an interferogram. We present here a two-dimensional (2D) SRWLI method that can be applied to measure narrow rectangle areas. A frequency comb is produced by using a Fabry-Perot (F-P) etalon to filter the broadband source. With the filtered frequency comb illumination, the interference patterns under adjacent wavelengths would be separated by a little distance, which enables us to obtain a 2D profile with a small width. The experimental details of measurement on a step sample are discussed in this paper.     

An algorithm for profilometry by white-light phase-shifting interferometry

Abstract

In the case of white-light interferometry, the usual phase shifting methods cannot be used because the modulation in the interference intensity is due to both the phase variation and to the coherence envelope. We propose a practical approach in which the coherence envelope is considered as locally linear. The classical four-point calculation algorithm is adapted to a set of seven intensities which are weighted with adapted coefficients in order to compensate for the effect of the coherence envelope. The capabilities of this method are described theoretically.     

Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry

A new method for measuring the birefringence dispersion in polarization-maintaining fibers (PMFs) with high sensitivity and accuracy is presented. The method employs white-light interferences between two orthogonally polarized modes of PMFs. The group birefringence of the fiber is calibrated first. Then the birefringence dispersion and its variation along different fiber sections are acquired by analyzing the broadening of interferograms at different fiber lengths. The main sources of error are investigated. Birefringence dispersions of two PANDA fibers at their operation wavelength are measured to be 0.011 ps/(km nm) and 0.018 ps/(km nm). A measurement repeatability of 0.001 ps/(km nm) is achieved.     

Rotation angle measurement based on white-light interferometry with a standard optical flat

We propose a simple white-light interferometric method of measuring a one-dimensional rotation angle with use of an optical plane parallel plate of standard refractive index. The phase change of the interference pattern of the interferometer during the rotation of the flat plate of known refractive index and thickness placed in one of the interferometer's arms is used for determination of the rotation angle. This method has been demonstrated for an accurate angle measurement over the angle range from 0° to 40° within a maximum uncertainty of 0.057°.     

Fast surface profiling by spectral analysis of white-light interferograms with fourier transform spectroscopy

We present a fast white-light interference method for measuring surface depth profiles at nanometer scales. Previously reported white-light profilers have relied either on path difference scanning or on spectral analysis of the reflection from a fixed interferometer. We show that by performing this spectral analysis with an imaging Fourier transform spectrometer, the high speed of spectral techniques may be combined with the simple data interpretation characteristic of the scanning method. Giving experimental results from a profiler based on this principle, we show that real-time visualization of surface profiles is possible and we report measurements with a repeatability of approximately 5 nm rms. We also demonstrate good agreement with stylus profiler measurements.     

Improved white-light interferometry on rough surfaces by statistically independent speckle patterns

White-light interferometry (WLI) on rough surfaces is based on interference from individual speckles. The measurement uncertainty of WLI is limited by a random shift of these individual interference patterns. The statistical error in each measurement point depends on the brightness of the corresponding speckle: a dark speckle yields a larger error than a bright speckle. In this paper, a novel method is presented to reduce the measurement uncertainty significantly: by sequentially switching the direction of the illumination, the camera sees several independent speckle patterns in sequence. From each pattern, the brightest speckles are selected to eventually calculate an accurate height map. This height map displays no outliers, and the measured surface roughness is close to the stylus measurements.     

Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry

White-light scanning interferometry is increasingly used for precision profile metrology of engineering surfaces, but its current applications are limited primarily to opaque surfaces with relatively simple optical reflection behavior. A new attempt is made to extend the interferometric method to the thickness-profile measurement of transparent thin-film layers. An extensive frequency-domain analysis of multiple reflection is performed to allow both the top and the bottom interfaces of a thin-film layer to be measured independently at the same time by the nonlinear least-squares technique. This rigorous approach provides not only point-by-point thickness probing but also complete volumetric film profiles digitized in three dimensions.     

Measurement of a fiber-end surface profile by use of phase-shifting laser interferometry

We describe a laser interferometric system in which two objectives are used to measure surface profile on a connectorized fiber-end surface. By the use of the proposed illumination design a He-Ne laser as a point light source is transformed to an extended light source, which is beneficial to localize interference fringe pattern near the test surface. To obtain an optimal contrast of the interference fringe pattern, the flat mirror with an adjustable reflection ratio is used to suit different test surfaces. A piezoelectric transducer attached on the reference mirror can move precisely along the optical axis of the objective and permits implementation of four-step phase-shifting interferometry without changing the relative position between the CCD sensor and the test surface. Therefore, an absolutely constant optical magnification can be accurately kept to capture the interference fringe patterns resulting from a combination of light reflected from both the reference flat mirror and the test surface. The experimental result shows that surface profile on a fiber-end with surface features such as a small fiber diameter of 125 microm and a low reflection ratio of less than 4% are measurable. Measurements on a standard calibration ball show that the accuracy of the proposed setup is comparable with that of existing white-light interferometers and stylus profilometers.     

Determination of the instrument function of a grating spectrometer by using white-light interferometry

We determined the instrument function or the response function of a grating spectrometer with finite slit widths in conditions of partial coherent illumination, by using a spectral-interference technique with white light. A Michelson interferometer of variable path delay is used to produce the spectral-interference fringes of required spacing. By deconvolution of the spectral visibility data for various exit and entrance slit widths, we have determined the exact form and frequency width of the instrument function for the spectrometer as well as the working region of the spectrometer for the least distorted output spectrum.     

Dispersion measurement of tapered air-silica microstructure fiber by white-light interferometry

Dispersion properties of novel, tapered, air-silica microstructure fibers are measured between 1.3 and 1.65 microm by white-light interferometry. Dispersion values (beta2) of -181 and -152 ps2/km were obtained for 2.2- and 3-microm core sizes, respectively, at lambda = 1.55 microm.     

Measurement of the influence of dispersion on white-light interferometry

White-light interferometry is a well-established method for measuring the height profiles of samples with rough as well as with smooth surfaces. Because white-light interferometry uses broadband light sources, the problem of dispersion arises. Because the optical paths in the two interferometer arms cannot be balanced for all wavelengths, the white-light correlogram is distorted, which interferes with its evaluation. We investigate the influence of setup parameters on the shape of the correlogram. Calculated values are compared with experimental results.     

Theoretical measurement uncertainty of white-light interferometry on rough surfaces

A great advantage of the white-light interferometry is that it can be used for profile objects with a rough surface. A speckle pattern that arises in the image plane allows one to observethe interference; however, this pattern is also the source of the measurement uncertainty. We derive the theoretical limits of the longitudinal uncertainty by virtue of the first-order statistics of thespeckle pattern. It is shown that this uncertainty depends on the surface roughness of the measured object only; it does not depend on the setup parameters.     

Direct measurement of refractive-index dispersion of transparent media by white-light interferometry

We report on a technique for measuring the refractive indices of nonabsorbing media over a broad spectral range from 0.5 to 5 microm. White-light interferometry based on a double-interferometer system consisting of a fixed Mach-Zehnder interferometer and a Fourier-transform spectrometer is used for direct measurement of the absolute rotation-dependent phase shift induced by an optical element. Refractive index n(lambda) over the whole investigated spectral range is thus obtained directly to an accuracy of 10(-4) without the need for any specific assumption about dispersion. Results for synthetic fused silica are presented and discussed.     

Sensitivity analysis of thin-film thickness measurement by vertical scanning white-light interferometry

The spectral nonlinear phase method and the Fourier amplitude method have been applied to measure the thin-film thickness profile in vertical scanning white-light interferometry (VSWLI). However, both the methods have their disadvantages, and accordingly their applications are limited. In the paper we have investigated the dependence of the sensitivities of both the methods on the thin-film thickness and refractive index, the objective numerical aperture, and the incident light spectral range of VSWLI. The relation of the Fresnel reflection coefficients on the wavelength effect is also discussed. Some important research results reveal that the combination of both Fourier amplitude and nonlinear phase methods may provide a new approach to improve the VSWLI measurement sensitivity for thin-film thickness profile.     

Evaluation of the focal distance of lenses by white-light Lau phase interferometry

We used a white-light Lau phase interferometer to evaluate the focal distances of two lenses. We found that the variation in the experimentally measured value is less than +/-1% from the given values. Limitations of the method and error analysis are presented.     

Experimental study of the phase-shift miscalibration error in phase-shifting interferometry: use of a spectrally resolved white-light interferometer

The white-light interferogram in a spectrally resolved white-light interferometer is decomposed in its constituent spectral components by a spectrometer and displayed along its chromaticity axis. A piezoelectric transducer phase shifter in such an interferometer can give a desired phase shift of pi/2 only at one wavelength. The phase shift varies continuously at all other wavelengths along the chromaticity axis. This situation is ideal for an experimental study of the phase error due to the phase-shift error in the phase-shifting technique, as it will be shown in this paper.     

Estimating wind speed in the lower atmosphere wind profiler based on a genetic algorithm

A lower atmosphere wind profiler, which is a pulse Doppler radar, is a useful operational tool that can provide unattended and continuous observation of wind profiles. Since the observed signals are usually degraded by ground clutters which are overlapped with the wind signal, it is necessary to develop a method to estimate the wind signal from the observed signals. In this paper, we propose to use a genetic algorithm to resolve the overlapping signals.     

Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path

We describe what is to our knowledge a novel technique for phase unwrapping. Several algorithms based on unwrapping the most-reliable pixels first have been proposed. These were restricted to continuous paths and were subject to difficulties in defining a starting pixel. The technique described here uses a different type of reliability function and does not follow a continuous path to perform the unwrapping operation. The technique is explained in detail and illustrated with a number of examples.