We propose a model for coherence scanning interferometry using familiar Fourier optics methods and the spectrum of plane waves for the case where light source spectral bandwidth limits the fringe contrast as a function of optical path length. The model is straightforward to implement, is computationally efficient, and reveals many of the common error sources related to the optical filtering properties of the imaging system. We quantify the limits of applicability of the model related to the geometrical approximations for Fourier optics, particularly for high numerical apertures, and when using the fringe contrast for determining surface heights. These limitations can be overcome using a three-dimensional imaging model.
We propose an instrument model for coherence scanning interferometry using familiar Fourier optics methods, the spectrum of plane waves, and the assumption that the light source spectral bandwidth is the dominant factor in determining fringe contrast as a function of optical path length. The model is straightforward to implement, is computationally efficient, and reveals many of the common error sources related to the optical filtering properties of the imaging system. We quantify the limits of applicability of the model related to the geometrical approximations for conventional Fourier optics, particularly for high numerical apertures, and when using the fringe contrast for determining surface heights. These limitations can be overcome by using a three-dimensional imaging model.
Interferometers for the measurement of topography rely on imaging systems to map surface points to a camera. The response of an interferometer to variations in surface height depends on the filtering properties of the imaging system. Here we provide a simple and practical model of an imaging interferometer using classical Fourier optics, including the effects of partial coherence. The model is useful for understanding basic properties such as lateral resolution and error sources related to measurement principles that make assumptions regarding the fidelity of the instrument response over a range of surface spatial frequencies and light source wavelengths.
Optical non-contact, interferometric measurement strategies for mold pins and plates provide an effective means for improving the consistency of the injection molding of small lenses for consumer devices. In this presentation, we describe high-precision interferometric metrology combined with motion systems and advanced software to address the wide range of length scales and metrology requirements of mold assemblies intended for high-volume production.
Injection molding is the leading high-volume production method for aspheric lenses used in consumer electronics. The design tolerances of these lenses require careful metrology of pins, resultant lenses and the injection molding plates themselves. Pins determine the form of the lenses, while the alignment of the pins to the mold plate determines apex distance, decenter and tilt. One key parameter of the mold plate is the overall flatness, as it is a critical datum for the pins. We demonstrate flatness metrology on a platform capable of sub-micron lateral resolution that can be used for roughness measurements as well as high resolution measurements of sub-millimeter features such as apex centration. The platform is capable of measuring the full 200 mm by 200 mm mold plate in under 30 minutes. The flatness results are correlated with measurements from a laser Fizeau interferometer and demonstrate better than ±1 μm correlation on samples with 20 microns of departure and better than ±0.2 μm correlation on plates with sub-micron departure.
KEYWORDS: Interferometry, Modulation transfer functions, Interferometers, Imaging systems, 3D modeling, Spatial frequencies, Diffraction, Reflectivity, Point spread functions, 3D metrology
Interferometers for the measurement of surface form and texture have a reputation for high performance. However, the results for many types of surface features can deviate from the expectation of one cycle of phase shift per half wavelength of surface height. Here we review the fundamentals of imaging interferometry and describe ways of defining instrument response, including the linear instrument transfer function. These considerations define practical regimes of linear behavior that are usually satisfied for traditional uses of interferometers; but that are increasingly challenged by applications involving complex textures and high surface slopes. We conclude by proposing pathways for further improving performance on difficult surface structures using advanced modeling techniques.
Optical 3D profilers based on Coherence Scanning Interferometry (CSI) provide high-resolution non-contact metrology
for a broad range of applications. Capture of true color information together with 3D topography enables the detection of
defects, blemishes or discolorations that are not as easily identified in topography data alone. Uses for true color 3D
imaging include image segmentation, detection of dissimilar materials and edge enhancement. This paper discusses the
pros and cons of color capture using standard color detectors and presents an alternative solution that does not rely on
color filters at the camera, thus preserving the high lateral and vertical resolution of CSI instruments.
We have developed a scanning white-light interference microscope that offers two complementary modes of operation
on a common metrology platform. The first mode measures the topography and the second mode measures the complex
reflectivity of an object surface over a range of wavelengths, angles of incidence and polarization states. This second
mode characterizes material optical properties and determines film thickness in multi-layer film stacks with an effective
measurement spot size typically smaller than 10 μm. These data compensate for material and film effects in the surface
topography data collected in the first mode. We illustrate the application of this dual-mode technology for post-CMP
production-line metrology for the data storage industry. Our tool concurrently measures critical layer thickness and step
height for this application. The accuracy of the latter measurement is confirmed by correlation to AFM measurements.
A white-light interferometer with new signal analysis techniques provides 3D top surface and thickness profiles of
transparent films. With an additional change from conventional object imaging to pupil-plane imaging, the same
instrument platform provides detailed properties of multilayer film stacks, including material optical properties. These
capabilities complement conventional surface-topography measurements on the same platform, resulting in a highly
flexible tool.
Pupil-Plane Scanning White-Light Interferometry measures reflectivity as a function of angle of incidence, wavelength
and polarization in one location of an object surface. This information is converted into ellipsometric information and
allows the characterization of material optical properties and layer thickness in the case of layered structures. We
illustrate the capability of the method by measuring the thickness and refractive index of thin film standards. The
information is also used to create accurate 3D topography maps of complex object structures.
A theoretical model of the optical system of an interference microscope includes both geometrical and spectral contributions to fringe contrast localization. An incoherent superposition of interference patterns over a range of wavelengths and pupil-plane coordinates predicts the frequency-domain portrait of the interference phenomenon. An inverse Fourier transform then provides simulated signals that correlate very closely to experimental data. The model is particularly useful for signal prediction, algorithm testing, uncertainty analysis and system characterization, including modern applications in thin film analysis and stroboscopic interferometry.
We report on characterization techniques for microstructures using white-light interference microscopy. Capabilities include surface profilometry, integrated profilometry and lateral metrology for full 3D characterization, defect detection, profilometry of thin film structures, stroboscopic interferometry of vibrating samples, and real-time profile snapshots of moving MEMS devices.
The processing of low-coherence interferometric signals in the frequency domain generates multiple images of an object surface, each image corresponding to a distinct wavelength or illumination angle. The detection of the motion of object features between images provides a direct measure of the net effect of chromatic and some geometric imaging aberrations. The data are presented as vector plots showing the motion of the centroid of imaging ray bundles as a function of wavelength or illumination angle, and as a function of field position. The correlation technique developed for this application resolves feature motions smaller than the optical resolution of the imaging system. The approach is applied to the characterization of high and low numerical aperture interference microscope objectives. The information can be used to minimize misalignments of an interferometer, compare the performance of lenses and offer objective means of assessing the potential lateral resolution of an instrument.
We compare two modes of measurement of shallow objects using a scanning interference microscope. In one mode the object is moved with respect to the Mirau interference objective while a camera records the interference pattern. In another mode the beam splitter is moved during the scan while the object remains in focus. We use both narrowband and broadband extended LED sources for the experiments with a modified 0.8-NA Mirau objective. A detailed analysis of the low-coherence interference signals in the spatial and spectral domains reveals small differences between the two scan mode. However, the comparison of surface profiles of objects having surface departures smaller than the depth of focus shows no appreciable differences. We conclude that the small amount of defocus that affects interference signals recorded during an object scan does not influence the quality of the measurement when using typical broadband extended sources.
Bragg Gratings are waveguides, typically single-mode optical fibers, into which a periodic refractive index modulation has been imprinted by a patterned UV exposure. Fiber Bragg Gratings separate telecom frequency bands or compensate for optical dispersion in long-haul fiber networks, and also serve as strain sensors for civil engineering or geophysical studies and oil, gas or mining exploitation. A Bragg Grating writer is an interferometer for generating the UV exposure pattern. It is one of the unusual cases where an interferometer is a production tool, rather than a metrology instrument. In this paper, we review the most common Bragg Grating writing geometry and propose an opto-mechanical structure having minimal adjustment and very high mechanical stability.
We describe techniques for measuring step heights between separated, nominally plane-parallel surface regions of a precision-engineered part. Our technique combines a broadband, 10-micron wavelength scanning interferometric profiler with a HeNe laser displacement gage. The infrared wavelength accommodates machined metal parts having a surface roughness in excess of what would be possible with a visible-wavelength interferometer. The combination of broadband interferometry, which removes fringe order ambiguity, with a laser displacement gage makes it possible to determine the relative heights of surfaces separated by several mm with a 2-σ uncertainty of 0.3 micron. We present the instrument theory, experimental implementation and results of instrument testing.
The measurement of shape, displacement and deformations is often performed using interferometric methods, featuring nm to mm sensitivities and very high spatial and temporal resolutions. We first give a brief overview of interferometric techniques. Emphasis is laid on the wide purposes of these techniques. Then, we present a novel method using wavelet analysis to process live interference patterns. Further developments of the method are then presented. Finally, through two practical examples, we intend to highlight the interest of fringe processing by wavelet transform.
We describe the detailed design of a geometrically desensitized interferometer using two transmission diffraction gratings. A number of models of the instrument are used to eliminate object ghosts and stray light contributions. We then investigate analytically the influence of object slope variations on the instrument precision. We show that the part can be located at a measurement location where the metrology is optimized. Analytical and raytracing models demonstrate excellent agreement with experiment.
A geometrically desensitized interferometer (GDI) uses two beams incident on the same sample area at different angles of incident to generate an interference pattern with an equivalence wavelength larger than the illumination wavelength. The instrument is well adapted to the metrology of both smooth and rough samples that are beyond the range of conventional interferometers, while providing more accuracy than conventional moire techniques. In this paper, we extend the capabilities of a GDI with an equivalent wavelength of 12.5 micron using coherence scanning in a manner similar to that of scanning white light interferometry. We also present new analysis techniques to accommodate speckle phenomena that can be more prominent in GDI than in white light interferometry. Our scanning GDI can rapidly characterize the surface flatness and relative heights of discontinuous surface features over large measurement volumes.
Geometrically desensitized interferometry uses two beams at different incident angles to generate an interference pattern with an equivalent wavelength of 5 to 20 micrometers. Unlike conventional interferometers, the fringe contrast is primarily a function of the optical geometry, rather than the spectral properties of the source light. In particular, a line-shaped source provides either a narrow or broad contrast envelope, depending on the orientation of the line with respect to the plane of incidence. This adjustable coherence depth is useful for initial system alignment, depth scanning and for separating surfaces of transparent flat parts.
The mechanical behavior of satellite telescope structures, subjected to non-uniform heating, as this occurs in orbit, is examined. In the laboratory, temperature gradients are created either by resistors or by IR lamps. Telescope structures are made of a material of very low thermal expansion coefficient--INVAR or carbon-carbon composite--in order to cope with stringent long term stability requirements in relation to temperature variation. Real time holographic interferometry is used to disclose the micro- deformation of the telescope. A careful implementation of the method is necessary, since, within the fixed temperature range for this study, very small deformations are expected. Monitoring of the heating conditions is achieved by an IR camera and thermocouples. Maps of temperature and of the corresponding interferometric out-of-plane deformation are obtained in parallel. The dynamic phase shifting technique allows to produce time-sequences of such deformation maps. These movies, and the temperature/deformation maps, highlight the structure deformation in a quantitative and dynamic way and suitably determine whether the structures meet their specifications.
A new method is presented that allows continuous deformation measurements to be performed. It is based on the use of the deformation-induced phase change produced at each pixel to compute an instantaneous phase with a dedicated phase- shifting algorithm. Examples in holographic, speckle and decorrelated speckle interferometry illustrate the interest of the method which provides both relative displacement phase maps and absolute temporal phase evolution curves.
An interferometer based on a single multi-functional holographic optical element (HOE) is presented. The interferometer is meant for flatness testing of quite large objects, not necessarily optically polished. Other features include two beam common-path arrangement, desensitization as compared to the classical (lambda) /2) figure, white-light illumination. Emphasis is then laid on automatic fringe pattern interpretation which makes use of an ad hoc phase-shifting procedure. Results obtained with computer disks are shown.
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