This PDF file contains the front matter associated with SPIE Proceedings Volume 7063, including the Title Page, Copyright information, Table of Contents, Introduction (if any), and the Conference Committee listing.

There is now a global interest in the creation of creation of electromagnetic metamaterials. The substantive early work is focused upon the GHz frequency range but almost immediately the desire to progress rapidly to the optical frequency range gathered momentum. This is a natural desire because many applications operate at optical frequencies but the THz range is also important for a range of medical applications as well. The concepts that underpin the need for metamaterials, and their special properties, are explained in this article and why the creation of exotic, artificial, molecules is required to produce material behaviour beyond any performance that could naturally be expected. It will be shown that the major key lies in adding magnetic properties to special dielectric behaviour. This leads to composites that have almost magical behaviour. This presentation will explore the current global experimental progress towards three-dimensional metamaterials and will explain, in a straightforward manner, the concept of negative refraction that is attracting such a lot of attention. The initial ideas, and even some of the early misconceptions, will be addressed and clearly illustrated in a manner that enhances any understanding of the conceptual structure will be expressed. It will be shown that even though negative refraction can be associated with both backward and forward waves, the novel metamaterial concept is to associate backward wave phenomena with isotropic media, artificially endowed with negative permittivity and permeability. The principle application shown here is to a nonlinear ring interferometer that is capable of sustaining arbitrarily thin solitons or "optical needles" that can also be managed by an external magnetic field.

Real wedge interferometers of the Fizeau-type do not allow for fringes in case of a spectral broad band source - or in short: for white light fringes. Here, the use of a suitable frequency comb source will help to overcome this limitation on the one hand and on the other will offer the capability for enhanced phase sensitivity in high precision measurements of surface deviations. Frequency combs can be produced either by using a pulse train from a fs-laser or by passive filtering of the light emitted by a broad band source as a superlum-diode or a fs-laser. The frequency comb produced by a common fs-laser is extremely fine, i.e., the frequency difference of consecutive peaks is very small or the distance of consecutive pulses of the pulse train might be of the order of 1m. Therefore, the coarse pulse train produced by passive filtering of a broad band source is better adapted to the needs of surface testing interferometers. White light fringes are either applied for the profiling of discontinuous surfaces and/or can serve as an indication for the correct choice of multiplication factors in superposition interferometry. During the last decennium it became more and more clear that spatially incoherent sources provide better measuring accuracy in surface measurements due to the reduced influence of dust diffraction patterns. The advantage of laser illumination can nevertheless be maintained if the laser light is made spatially incoherent through moving scatterers in the light path. Here, we will discuss the application of spatially incoherent broad band light frequency filtered through a Fabry-Perot filter. The main applications are in the following fields: (1) surface profiling applications using two-beam Fizeau interferometers, (2) selection of single cavities out of a series of interlaced cavities, and (3) sensitivity enhancement for multi-beam interferometers for planeness or sphericity measurements. Some of the discussed possibilities will be experimentally demonstrated.

All two-beam interferometry eventually reduces to quantitative measurement of the effective fringe visibility (or degree of coherence) in some form. We present generalized analytical and experimental results of visibility for the cases of two beam Poynting vectors both collinear (scanning fringe mode) and non-collinear (spatial fringe mode) with different polarizations and frequencies. This leads to a much broader and deeper understanding of the roles of material dipoles (beam splitters & detectors; both classical and quantum) in measured coherence effects that are not explicitly addressed in the traditional coherence theory. Coherence theory should be presented as correlation between sensing dipole undulations that are simultaneously induced by superposed light beams rather than as correlation between the optical fields. This generalized understanding of the physical processes behind coherence phenomenon will open up (i) better understanding of the nature of light and (ii) many more innovative approaches to quantitative interferometry.

The Spatially Phase Shifted Digital Speckle Pattern Interferometer (SPS-DSPI) is a speckle pattern interferometer in which the four phase-shifted interferograms are captured simultaneously in a single image. Designed to measure thermal distortions of large matte-surfaced structures for the James Webb Space Telescope (JWST) program, this metrology instrument has been used in two major cryo-distortion tests. This report will describe how differences in the vibrational motions of the test objects necessitated changes in basic algorithms. The authors also report operational upgrades, quantification of uncertainty, and improvement of the software operability with a graphic interface. Results from the tests of the JWST test structures are discussed as illustration.

An on-axis, vibration insensitive, polarization Fizeau interferometer is realized through the use of a pixelated polarization mask spatial carrier phase shifting technique in conjunction with a high coherence source and a polarization frequency shift device. In this arrangement, differential motion between the test and reference surfaces, in conjunction with the polarization frequency shift device, is used to effectively separate 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. Additionally, the use of a high coherence source eliminates the need to path match the test and reference arms of the interferometer. Using a 1 mW HeNe source, the optimum camera shutter speed, used when measuring a 4% reflector, was 250 usec, resulting in significantly reduced vibration sensitivity. Experimental results show the performance of this new interferometer to be within the specifications of commercial phase shifting interferometers.

Quantitative surface strain measurement is demonstrated on dynamic test objects using a shearography instrument comprising four measurement channels. The measurement channels are formed using four observation directions and a single illumination direction. Images from the four measurement channels are transported to a shearing interferometer using fibre-optic imaging bundles after which they are spatially multiplexed onto the quadrants of a single CCD camera. This facilitates the simultaneous acquisition of data from the four measurement channels. A pulsed laser source was used to effectively freeze the motion of the dynamic surface at two positions in its cycle. The phase variation caused by surface deformation in the time between the two recordings was calculated using the spatial carrier technique. The orthogonal displacement gradient components which characterize the surface strain of the object were calculated from the unwrapped phase maps from each measurement channel using a matrix transformation. Two test objects were investigated. The first was a thermally loaded PTFE plate rotating at 610 rpm. Images were recorded a frequency of 10 Hz, corresponding to the repetition rate of the laser. The second object was a speaker cone that was set to vibrate at frequencies in the range of 1.9-4.5 kHz. Phase measurements were made from images recorded 1.6 μs apart using dual pulsed illumination in combination with a dual-framing CCD camera.

Lateral shearing interferometers (LSIs) are efficient tools for optical analysis. They allow classical optical wave-front aberrations measurements as well as the precise evaluation of abrupt steps. The basic element of an LSI is the transmittance grating, which diffracts a number of orders (two in the case of a mono-dimensional LSI, ideally three or four non coplanar orders in the case of bi-dimensional LSI). This brings the need for specifically designed transmittance gratings. For instance, a mono-dimensional LSI needs a sinusoidal-shaped transmittance, since its Fourier transform carries exactly 2 orders. Such transmittances are however either impossible or at least extremely costly to design using classical macroscopic techniques, mainly because the usual thin film deposition techniques require several technological steps, in order to get the desired light filtering effect. Given these constraints, we made use of sub-wavelength structures in order to build a new class of LSI. They are made of sub-wavelength lamellar metallic gratings specifically designed for the mid-infrared, and allow the precise coding of the desired transmission shape all over the LSI grating.

The novel measurement method based on the virtual speckle patterns has been reported. The method can analyze the phase map in high resolution by using only information concerning the change of intensity of each speckle during a deformation process. In this paper, the possibility of the application for the analysis of dynamic in-plane deformation measurement by the method is investigated. The measuring optical system for dynamic events is discussed. In the experimental results, the phenomenon of in-plane deformation by the collision of the metal sphere to a block of hard rubber is measured. The virtual speckle patterns are produced by only information during a deformation process in order to analyze the deformation process. It is confirmed that the new method can analyze a large deformation which could not analyze by the ordinary methods. Then, it is also confirmed that the high resolution measurement can be performed by this method. The measuring optical system for dynamic events is discussed.

In analogy with the degree of polarization used widely for the description of partially polarized thermal light, we introduced a new concept of the spatial degree of polarization to characterize the statistical properties of the polarization speckle with its polarization states fluctuating in space. As a function of the spatial degree of polarization, the first order statistics of the polarization speckle are studied theoretically, and the corresponding probability density functions of the Stokes parameters are measured experimentally by a polarization interferometer to demonstrate the validity of the principle.

Interferometrical methods like Shearography or Electronic-Speckle-Pattern-Interferometry (ESPI) are being used for remote deformation measurements. For non-destructive testing, usually not the deformation of the whole inspected object is of interest, but only the changes in the deformation field that are caused by hidden defects. By applying the lockin technique, small local discontinuities can be monitored even on a large background deformation. Dynamic excitation is performed by modulation of absorbed light intensity while object deformation is continuously recorded to give a stack of fringe images. Instead of using only the information contained in the image with the best contrast, our technique evaluates the whole image stack with respect to the local response to the coded input. The periodical component of the deformation is extracted by Fourier transformation for the time dependent signal at each pixel. This way the relevant information contained in the image stack is compressed to an amplitude- and a phase angle image. As only defects contribute to a signal change in the phase image, the method is defect selective. Furthermore, the phase change depends on depth where the defect is located since thermal waves are involved. One more advantage is the substantial improvement of the signal-to-noise ratio.

We present an introduction to the Bidimensional Empirical Mode Decomposition (BEMD) and its application to the denoising of DSPI fringes. The BEMD is based on the decomposition of an image in high and low frequency zero-mean oscillation modes, called intrinsic mode functions (IMFs). The decomposition is carried out through a sifting process which produces many few basis functions than the ones generated by the Fourier or the wavelet transforms. The denoising approach is based on the removal of the first IMFs, so that the filtered image is given by the residue. A normalization algorithm is then applied to the denoised fringes to reduce the oversmoothing caused by the filtering. The performance of this denoising approach was evaluated using computer-simulated DSPI fringes with different fringe density and speckle size, in order to calculate a figure of merit through the comparison with the noise-free fringes. The obtained results are also compared with those produced by other smoothing methods, and the advantages and limitations of the proposed approach are finally discussed.

Phase unwrapping is a usually necessary step in optical interferometry in order to construct a continuous phase distribution. A straightforward strategy is to filter the noise effectively, followed by a simple phase unwrapping process. A windowed Fourier filter is proposed to realize this strategy, which has the following properties: (i) it removes the noise effectively; (ii) it preserves the phase near edges; (iii) it identifies invalid areas; (iv) the amplitude of filtered exponential phase field can be used as a quality map for quality-guided phase unwrapping; (v) the filtering result is insensitive to the threshold; (vi) the window size in the filter can be switched according to different requirement. A large window size is useful for noise filtering while a small window size is useful for protecting signal details.

In order to control performance of photonics microelements it is necessary to receive 3D information about their amplitude and phase distributions. To perform this task we propose to apply tomography based on projections gather by digital holography (DH). Specifically the DH capability to register several angular views of the object during a single hologram capture is employed, which may in future shorten significantly the measurement time or even allow for tomographic analysis of dynamic media. However such a new approach brings a lot of new issues to be considered. Therefore, in this paper the method limitations, with special emphasis on holographic reconstruction process, are investigated through extensive numerical experiments with special focus on 3D refractive index distribution determination.. The main errors and means of their elimination are presented. The possibility of 3D refractive index distribution determination by means of DHT is proved numerically and experimentally.

In this paper, we proposed a calibration method with a reference plane to analyze strain distribution using three spherical waves in independent directions. The relationship between the phase difference and displacement for each pixel are determined for one beam using a reference plane. When this measurement is performed for each of three beams, the sensitivity matrix for each pixel can be obtained independently. We also proposed a phase analysis method using Fourier transform for a wave composed by three waves. Three spherical waves are irradiated onto the reference plane or an object simultaneously. The principle and the experimental results of strain measurement are shown.

The lack of commercial equipment for characterization of vibrating micro- and nanostructures has motivated the development of a heterodyne interferometer. The setup is designed to measure phase and absolute amplitude in the entire frequency range 0-1.2 GHz. Its transverse resolution is < 1 μm while the present sensitivity for vibrations is 3 pm/(Hz)^1/2. Capacitive micromachined ultrasonic transducers (CMUTs) are being developed for diagnostic imaging of vulnerable plaques in the coronary arteries. The CMUTs have 5.7 μm radii, 100 nm membrane thickness and ~30 MHz center frequency. Arrays of ~7500 CMUTs have been fabricated. Frequency scan measurements along a row of CMUTs reveal a variation in resonance frequency. This may be due to variations of material properties, dimensions such as thickness and transverse dimensions, and other manufacturing variance. The frequency scan revealed the fundamental mode and two closely spaced higher order modes. Modeling of individual CMUT elements was performed using the commercial program COMSOL. A finite element model (FEM) based on symmetry assumptions predicted only one higher order mode. After closer analysis it was found that the symmetry assumptions were insufficient. By using a complete physical model two higher order modes were predicted in agreement with the measurements. Simulations are able to predict transducer characteristics in great detail but are dependent on accurate input parameters. The optical measurements contribute to validate or complement simulations and assumptions they rely on. The heterodyne interferometer is therefore a valuable tool for quality control in the conception, design and manufacturing of new acoustic devices.

We propose a new out-of-plane vibration imaging technique for micro-structured solid-state devices such as MEMS (microelectro mechanical systems) microphones and resonators. This technique is based on the longitudinally scanning optical interferometry and an integrated image sensor device which we call the correlation image sensor (CIS). The CIS is able to extract an arbitrary frequency component from time-varying incident light and produce a complex correlation image including amplitude and phase in addition to a conventional intensity image. In heterodyne interferometry of vibrating objects, the vibration information is encoded in several frequency components generated by mutual modulation of longitudinal scan and vibration. In this paper, the combination of newly developed multi-channel CIS and the scanning heterodyne technique enable us to obtain the multiple frequency components simultaneously and reconstruct the vibration amplitude and phase distributions in real time. As an example, vibration modes of a MEMS acoustic sensor are shown to be rconstructed at video rate. A theoretical possiblitiy for the imaging of higher than GHz vibration combining other optical heterodyne techniques is also discussed.

In this paper, a novel profiling method, Laser Confocal Feedback Profilometery (LCFP), combining quasi-common-path heterodyne phase detection with laser confocal feedback technology, is proposed. A microchip Nd:YAG laser emits 1064nm laser, which passes through a pinhole and frequency shifter, and is focused onto the sample surface. The reflected light is coupled back to the microchip laser cavity and forms the frequency shifted feedback light, causing the laser intensity modulation. When the sample is scanned laterally, its surface height variation changes both the phase and strength of the feedback light. LCFP then extracts both the amplitude and phase information out of the laser intensity modulation to determine the integral and fractional number of half laser wavelengths contained in the height variation of two points on the sample surface. LCFP can thus overcome the half-laser-wavelength limit of phase measurement in the axial direction. The high sensitivity of microchip laser to feedback light makes LCFP able to measure samples with very low reflectivity. The LCFP experimental setup is built, and it has successfully measured the height of the stages on a glass-substrate grating. The current performances of LCFP are as followed: the axial resolution is better than 2nm, the axial range about 5μm, and the detectable reflectivity as low as 10^-9. Due to its direct traceability to laser wavelength, LCFP can potentially be used as the metrology standard of small-scale features.

An alternative to the conventional linear phase shift in optical testing interferometers is a sinusoidal phase shift, which has the benefit of relaxing requirements on the phase-shifting mechanism. We propose new phase-demodulation algorithms and provide sensitivity analyses to random noise, nonlinearity, vibrations and calibration error to demonstrate that sinusoidal phase shifting can be as robust and computationally efficient as the more established linear phase-shift techniques.

While phase shifting interferometry (PSI) has clearly established itself as a powerful tool for surface profiling, two main experimental drawbacks still exist, namely phase-shift errors and non-sinusoidal interferometric signals. These problems cause a fringe print-through pattern in measured phase having a frequency typically double the original fringe frequency. The main tool used to compensate for non-linear phase-shift errors is the least-square phase-stepping method, which is capable of accurately determining the phase separation between consecutive frames as well as phase distribution for each frame. Our work here extends the capabilities of this algorithm so as to account for the effects of a wide bandwidth light source and a higher numerical aperture, which make the interference signal deviate from the ideal sinusoidal signal. We present a simple variable change mechanism that overcomes the coupling that occurs between the planar and depth coordinates and allows for a seamless integration with the standard least-square procedure.

Capturing 3-D geometry and the perfectly aligned color texture simultaneously is crucial for diverse fields including entertainment, target recognition, and computer graphics. However, it is very challenging for a conventional technique because of a number of problems related to color. Previous researchers rely heavily on using two cameras: a black-and-white(B/W) camera to measure the geometry, and a color camera to capture the color texture. However, aligning the color image with the 3-D geometry point by point remains difficult. In this research, we propose a novel technique that uses a single-chip color camera to capture both geometry and color texture simultaneously. A projector projects B/W fringe patterns onto the object, and a color camera captures the raw fringe images with Bayer mosaic patterns. A phase-shifting algorithm is used for our system because of one of its merits: retrieving phase pixel-by-pixel. Therefore, the intensity variations between neighboring pixels do not significantly affect the measurement. Moreover, the same set of fringe images is also used to calculate the B/W texture image, which is further converted into a color image using a demosaicing algorithm. Therefore, the same set of fringe images are used to generate the 3-D geometry as well as the color texture image simultaneously. A hardware system was developed to verify the performance of the proposed technique. Experiments demonstrated that this technique can successfully measure both geometry and color texture of the color objects.

In this paper, we present a novel method to measure shape and colour information of a colourful object by projecting separate red, green and blue colour fringe patterns onto the object surface. With regard to the object surface's colour, the modulation at each pixel position in the three colour channels has different values. For example, when projecting blue fringe patterns onto a red point, the corresponding pixel has too low a fringe modulation to accurately calculate the phase (shape) information; but with red fringe patterns a high fringe modulation is obtained. Therefore, phase information of the red point can be calculated by projecting red fringe patterns. For each object point, by comparing the modulation values from the three colour channels, it is possible to choose the channel having maximum modulation, and hence phase information can be reliably obtained by the phase-shifting algorithm. The fringe order information is obtained by using the optimum three-frequency selection method, so there is a maximum reliability in determining the fringe order and the 3-D shape of an object with step or large slopes on the surface. Since three colour channels are used, colour information of the object surface can be extracted with high dynamic range from the same fringe patterns. Chromatic aberration between colour channels is unavoidable and can be eliminated by a software-based method. Using the recently developed colour fringe projection system, separate colour fringe patterns are projected onto a mug having different colour patterns, a colourful box and plate, and a colour checker card to test the proposed method. The results show the range of colours that can be measured and that shape and colour information of colourful objects can be reliably obtained.

A projection moiré topography using two liquid crystal (LC) grating devices is proposed using frequency modulation. The moiré contour can be obtained by changing the LC grating pitch. It is possible to remove the original grating by electrically varying the period and averaging appropriately. Both a frequency modulation and a phase shift technique are applicable to this system because of the LC grating device. Some experimental results are presented.

In this paper we present our proposal of processing three-beam interferograms obtained in a Fizeau interferometer when testing quasi-parallel optical plates. If the intensities of three interfering beams reflected from the front and back surfaces of the investigated plates and from the reference flat are nearly equal, the modulation distribution of the pattern encodes the information of the plate optical thickness variations, whereas the phase distribution contains the information about the sum of profiles of both surfaces (uniform refractive index distribution is assumed). Both maps can be derived using a combination of different interferogram analysis techniques such as Temporal or Spatial Carrier Phase Shifting and Vortex Transform. As a result separate information about both surfaces from a single measurement can be obtained. The situation complicates, however, when noticeable difference of the beam intensities occurs. We prove that in this case the modulation still contain useful information on the optical thickness of the investigated plate. Numerical studies of the method working principle are complemented by experimental results.

The principle of angle-resolved reflectometry is exploited for thin-film thickness measurements. Within an optical microscope equipped with a high NA objective, a sequence of quasi-monochromatic light of different wavelengths is generated from a white-light source through spectral filters. Then for each wavelength, the reflectance intensity from the thin-film sample is monitored on the back focal plane of the objective. This enables collection of reflectance with varying incident angles. The film thickness is then uniquely determined by fitting the measured data to an ideal multi-reflection model of thin films. This method can be readily extended to multi-layered film structures, finding applications for industrial inspection of semiconductor devices and flat panel display products.

Wavelength scanning interferometry offers many advantages over traditional phase shifting interferometry, most significantly the elimination of mechanical movement of the part/s for phase modulation by implementing a tunable light source. Further, Fourier analysis on the interference time history enables this technique to accurately measure distances, treating the distance between two optical surfaces as an interferometric cavity. We propose to evaluate the uncertainty in the thickness measurement of a transparent cavity using a commercial Fizeau wavelength scanning interferometer. This work follows the theory and measurement performed in a previous manuscript of measuring absolute distances of opaque objects using a commercial wavelength scanning interferometer. The limits in measuring a cavity using the commercial wavelength scanning interferometer depend on many factors such as temperature variations that affect the test and reference cavity, uncertainty in the reference cavity calibration, tuning rate non-linearities, etc. In addition to an analytical approach, a simulation is described to better understand the measurement process and the uncertainty associated in measuring absolute distances (thickness) of cavities. Preliminary experimental results on the absolute thickness of a transparent cavity are reported along with uncertainty sources.

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.

Coherent absolute distance interferometry is one of the most interesting techniques for length metrology. In frequency sweeping interferometry (FSI), measurements are made without ambiguity, by using a synthetic wavelengths resulting from a frequency sweep. FSI-based sensors are simple devices and fulfill an important role on any demanding space mission metrological chain. Their parameterization flexibility allows either technological or application-related tradeoffs to be performed. Accuracy is mainly dependent on the capability to measure the synthetic wavelength, using a Fabry-Perot interferometer (FP) that counts resonances as the frequency sweeps, and on the number of detected synthetic fringes. For large ranges, the number of fringes dominates performances, leading to a linear decrease of the accuracy with range. By increasing the size of the interferometer reference arm, and by measuring both the distance and the reference arm independently, it is possible to ensure high accuracy for small distance measurements, even for much larger range. In the context of the ESA PROBA3 mission (coronagraph and demonstration of metrology for free-flying formation), we are prototyping a FSI sensor composed of a mode-hop free frequency sweep external cavity diode laser, a high finesse FP (to measure accurately the frequency sweep range) and a dual measurement system to enable the measurements at 150 m with an accuracy at the tens of micrometer level. Its uncertainty budget, interferometers design and preliminary experimental results are detailed in this paper.

A high accuracy surface inspection system for testing polished surfaces is based on a Fabry-Perot resonator. The inspected surface serves as a relay mirror in a cat-eye retroreflector incorporated into the resonating cavity, which makes the optical configuration insensitive to surface tilts. The laser wavelength is swept periodically over a given range, and the local surface height is obtained by timing the resonance occurrence during each sweep. An additional highly stable reference Fabry-Perot interferometer using the same laser is employed for obtaining differential measurements, yielding absolute height values, distinguishing between up and down defects. Due to the finesse of the multi-beam Fabry Perot interferometer relative to the two-beam Michelson interferometer response function, the height sensitivity is greatly enhanced. In order to detect small contamination particles, the interferometer was supplemented by a scattering detection channel integrated into the same compact optical head. The combination of the bright-field interferometric signal, yielding both the phase (surface height) and amplitude (surface reflectivity), and the dark-field scattering channel, allows one to build a sensitive and reliable defect detection and classification procedure. The interferometer was incorporated into high-speed high-accuracy in-line machines for inspection of the surfaces in data storage applications. With a 0.2 Angstroms resolution, the height rms repeatability at a surface scanning speed of 40 m/s is 1.5 Angstroms.

In this paper, we present an understanding of the failure modes of excess fractions solutions to multi-wavelength interferometry. From this basis, an approach to select optimum measurement wavelengths has been introduced. A practical fiber optic sensor has been constructed for simultaneous detection of the intensity at four measurement wavelengths. The system has been demonstrated using two wavelength selections that are very near the optimal configuration and the data analyzed using an excess fractions solver. Initial results have shown a measurement range of 17 mm with reliable and robust absolute metrology from a system with a phase noise of 1/200th of a fringe. This corresponds to an overall dynamic range of 1 part in 2×10⁶.

Interferometry is a well established technique for surface profiling. The conventional interferometric surface profilers using a single wavelength offer excellent vertical resolution, but a serious limitation to their use is that they can only handle smooth profiles and step heights less than half a wavelength. In the situation where the surface profile is discontinuous, white light interferometry has been applied with great success. However the scanning white light interferometry requires large number of frames to be recorded, whereas in spectrally resolved white light interferometry only a line profile of the object is obtained, although the requirement on number of frames is similar to the single wavelength phase shifting interferometry. In this paper we discuss three wavelength interferometry in which a limited number of frames suitable for phase shifting technique are recorded at three laser wavelengths. The phase evaluation at the three wavelengths gives wrapped phase at any pixel corresponding to these wavelengths. The fringe order is obtained considering the fact the variation of phase with wavenumber for a given profile height is linear. The slope of the phase verses wavenumber line gives the absolute value of the profile height and is used to ascertain the fringe order. The fringe order along with the wrapped phase gives the profile height with a resolution given by phase shifting technique. Experimental results on etched silicon samples are presented.

In this paper, we explore the optimization and implementation of multi-wavelength interferometers such that measurements beyond the largest beat wavelength can be achieved reliably. A hybrid beat wavelength approach is presented that also exploits wavelength coincidence between two beat wavelengths in order to measure unambiguously over an extended range. The performance of the approach has been explored both through simulations and experimental validation has been obtained using a fiber interferometer with 4 measurement wavelengths. The initial results have demonstrated 1/200th of a fringe phase resolution giving absolute metrology over 18.16 mm, or a dynamic range of 1 part in 2.4×10⁶.

Recently, the surface profiles of nanostructures have been reduced in size in order to develop microfabrication techniques, such as lithography and nanoimprinting. In particular, feature sizes of a few tens of nanometers are common in the semiconductor industry. This study uses a Mueller matrix polarimeter, which is based on a scatterometry technique, to evaluate the surface profiles of nanostructures. In this technique, a nanostructure profile is determined from the Mueller matrix which expresses all the polarization properties of the sample by experimental measurements and calculated values using rigorous coupled-wave analysis (RCWA). This technique is more useful than conventional scatterometry based on ellipsometry since it is able to determine the total polarization properties of a sample. This is because, the Mueller matrix is able to estimate the surface profile of a nanostructure to greater precision. The grating period of a Cr/Cr₂O₃ structure on a SiO₂ substrate was measured using a dual-rotating retarder polarimeter. The experimental results agree well with the values obtained by numerical analysis. We measured the characteristic of non-diagonal elements in the Mueller matrix by varying the incidence azimuth of the sample. We have demonstrated the possibility of evaluating a nanostructure profile from the Mueller matrix.

This study employed white-light interferometry to measure the three-dimensional (3D) profiles, roughness, and dimensions of brightness-enhanced films (BEFs) that exhibited roof-shaped profiles with large-bevel inclines that could not be successfully measured by conventional optical inspection. A scanning white-light interferometer (SWLI) was used to obtain image information from both the symmetrical sides of inclines in the BEFs. A feasible structure with an angle-tuning mechanism was also introduced to enable the scanning white-light interferometer to rotate the angle of vision according to the bevel angle of the incline in the BEF. Further, the profiles of the BEFs could be reconstructed successfully through a series of image processing techniques. Now, the allowable bevel angle of the inclines in the BEF is not greater than 45°. The experimental results confirmed that this approach can successfully measure the 3D profiles of large-bevel inclines of microstructures as well as the roughness and dimensions of BEFs.

We investigated the technical possibility of exploiting a femtosecond pulse laser as the light source of low-coherence interferometry for topographical inspection of silicon wafers. The intention was to measure both the front- and rear-surface profiles of a silicon wafer simultaneously by illuminating from one side of the wafer only. To the end, the spectrum of the femtosecond laser was widened using a photonic crystal fiber to yield wavelengths over the particular range of 1000 to 1200 nm, which is not only transmittable through silicon but also detectable by an ordinary CCD photodetector array. This tomographic scheme enables complete measurement of thickness profile and also detection of internal voids such as cracks residing inside the wafer with high lateral and depth resolutions, which could be useful for nondestructive testing of multi-layered packages of silicon wafers.

Fringe-resolved noncollinear autocorrelation extracts information about the pulse duration of ultrashort optical signals from analyzing the intensity envelope of fringes. By detecting nonlinear autocorrelation functions after frequency conversion, even an evaluation of temporal asymmetry and frequency chirp are enabled. Here we report on a modified approach based on replacing crossed plane waves by Bessel-like beams. In comparison to the conventional method, appropriate mathematical transforms have to be applied. The method is simple and single-shot capable and takes advantage of specific advantages of pseudo-nondiffracting beams. First proof-of-principle experiments with few-femtosecond pulse durations were performed and compared to simulations. In multishot operation regime, the implementation of phase-shifting procedures by spatial light modulators promises considerable improvements of the time resolution analogous to the known principle of phase-shift interferometry.

Methods to test on-axis and off-axis parabolic mirrors are standard textbook fare. All we need, we are told, is a spherical wavefront and a plane mirror, or a plane wavefront and a spherical mirror. Contrasting with the implied ease of application, reports on practical experience with these tests are somewhat rare, particularly for off-axis mirrors. We have explored both variations of this testing method with a phase-shifting Fizeau interferometer, auxiliary components, and a one-inch diamond-turned 90° off-axis commercial-quality parabolic test mirror. The testing process is quick and easy only if you know how, and frustrating and time-consuming otherwise. We report on the calibration of the reference surfaces, present a detailed and systematic re-appraisal of the necessary steps for alignment and measurement validation, which have been described previously but in a less straightforward way, and present a brief characterization of the parabolic mirror that gives some insight into the diamond-turning process.

We describe methods to correct both symmetric and asymmetric distortion mapping errors induced by null testing elements such as holograms or null lenses. We show experimental results for direct measurement and correction of symmetric mapping distortion, as well as an example result for analytical mapping performed using an orthogonal set of vector polynomials for asymmetric correction. The empirical determination of symmetric distortion is made via calculation from predicted and measured changes to aberrations induced via known changes to the testing point.

Interferometric surface tests of stigmatic aspherics can be carried out in a null test configuration. Null tests require reference null elements either plane or spherical surfaces or both. A parabolic reflector transforms a plane into a spherical wave which converges to the focus of the paraboloid. Therefore, a spherical ball lens or a steel ball can be placed into the focus enabling a double-pass geometry for the null test. Here a Fizeau interferometer geometry has been selected in order to guarantee invariance against polarization distortions under the assumption that radially polarized laser light is used for the interferometer. Radial polarized light is necessary to mimic a Hertzian dipole field. Due to the extreme solid angle produced by the paraboloid the alignment of the setup is very critical and needs auxiliary systems for the control. Aberrations caused by misalignments are removed via fitting of suitable functionals provided through ray-trace simulations. It turned out that the usual vector approximations fail under these extreme circumstances. Test results are given for a paraboloid with 2mm focal length transforming a plane wave into a near dipole wave comprising a solid angle of about 3,4π.

Frequently two-dimensional interferograms are obtained when a point-diffraction interferometer (PDI) is used in optical testing. The PDI is a simple, convenient and robust tool for optical shop testing. In this paper, we propose the use of the PDI and placing a slit at the exit pupil to scanning the surface under test. Stitching is then used to generate a phase map of the test wavefront. The advantage of the proposal is the sharpness of the fringes to obtain high resolution contour of the test wavefront, we describe the method and some experimental results.

Optical testing of a large convex aspheric surface, such as the secondary of a Ritchey-Chretien telescope, can be performed with a Fizeau interferometer that utilizes subaperture aspheric reference plates, each providing a null test of a subaperture of the larger mirror. The subaperture data can be combined or stitched together to create a map of the full surface. The region of the secondary mirror surface under test in each sub-aperture is an off-axis segment of the parent aspheric surface, therefore, the Fizeau reference requires a non-axi-symmetric aspheric surface to match it. Misalignment of the Fizeau reference relative to the parent in each sub-aperture will then result in aberrations in the measurements other than the ordinary terms of piston and tilt. When stitching sub-aperture measurements together, the apparent aberrations due to the null lens misalignment need to be fitted and subtracted. This paper presents an algorithm to perform this particular type of stitching.

A newly developed interferometer for characterization of aspheric surfaces is presented. The interferometer is based on the Fizeau configuration and uses a sub-Nyquist CCD camera as a detector. Due to the camera design, the instrument is capable of recording very dense fringe patterns of up to 4 fringes/pixel. This enables processing of interferograms with hundreds of fringes in the field of view. Thus, the interferometer can be used to measure many types of aspheric surfaces using a standard transmission sphere as a reference. However, the main obstacle associated with this kind of interferometer is caused by the presence of so called "re-trace" errors, which can be significant. Such errors occur from un-equal optical paths the reference and test beams travel through in the optical system of the interferometer. A ray tracing procedure has been developed to subtract the influence of the optical system of the interferometer on the measurement. This method of error compensation results in reducing measurement errors to λ/5 PV (peak to valley) for the full range of fringe densities with the low order aberrations not exceeding λ/10. We present measurements of test surfaces illustrating the effectiveness of the error compensation procedures as well as preliminary measurements of multiple aspheric surfaces.

A novel method for testing the collimation of coherent optical beam is presented. Two prisms are used to define a thin air wedge with a wedge angle. A wide range of beam sizes can be tested down to a few millimeters in diameter. By redirecting the transmitted beam back to the air wedge so that it experiences a shear in the reversed direction, a double-shearing interferometry can be established. The gap separation and wedge angle can be varied to maintain high sensitivity (twice that of the wedge plate design) over the wide beam size range.

Optical stochastic cooling (OSC) holds significant promise for cooling of charged particle beams to enhance the luminosity of high energy colliders. This paper describes the conceptual design and requirements for an interferometer to be built for an OSC demonstration experiment with stored electrons at the MIT-Bates South Hall Ring. The paper will present an overview of the optical and charged particle beamlines, the intensity detection system and the phase stabilizing feedback loop.

Laser encoders as an optical displacement measurement technique have many applications such as modern manufacturing, scanning probe microscopy (SPM) and nanomanipulation. For the measurement scale down to the nanometer range, the stability, sensitivity and tolerance to dynamic runout are the key issues for laser encoders. This paper presents a novel laser encoder for sub-nanometer displacement measurement. It is based on optical heterodyne interferometry and conjugate optics with a symmetric and quasi-common-path optical configuration. It offers high stability, high resolution, low uncertainty displacement measurements and can break through the dynamic runout problem in laser encoders. Experimental results reveal that the laser encoder can detect a displacement variation of 26 pm, and can thus be applied to sub-nanometer or even picometer positioning.

In our Optical Metrology laboratories, we deal with the problem of demodulating temporal sequences of interferograms. These sequences of interferograms are obtained by means of optical testing of transient events using an Electronic Speckle Pattern Interferometry system (ESPI). It is well known that using Phase Stepping Interferometry techniques (PSI), one can obtain the modulated interferogram phase with at least three equally temporal phase shifted interferograms. To obtain these three (or more than three) phase shifted interferograms with a conventional ESPI array, it is necessary to have a static object under test. On the other hand, if the object under test is not static, we can make the analysis using dual-pulse subtraction ESPI, introducing a spatial frequency carrier. However, in our case, we will use a conventional ESPI technique, with a continuous laser and without a frequency carrier. Thus, as we pretend to analyze transient deformations or events without frequency carrier, we can not use the demodulation methods used in dual-pulse subtraction ESPI, nor PSI techniques because it results almost impossible to take the least amount of interferograms with the required linear phase shift (or temporal carrier) among them. To accomplish this, it will be necessary look for alternatives to demodulate temporal sequences of interferograms without a frequency carrier and without linear phase-shifting. Here, we present the groundwork aimed at demodulating sequences of interferograms without a frequency carrier, where traditional PSI techniques are unable to detect the phase correctly.

Previous researches have shown that spatial coherence wavelets provide the phase-space representation for optical fields in any state of coherence and polarization and can represent the radiometric properties of optical sources. In this paper, we have developed a research about their holographic features and particularly we have found the cross-spectral density at the observation plane should be regarded as the second-order wave reconstructed from the Fourier hologram of the marginal power spectrum, where the power spectrum corresponds to the zeroth-order of the reconstruction and the characteristic hermiticity of the cross-spectral density determines the twin images. In a similar way, the holographic reconstruction of the cross-spectral density at the aperture plane has been stated, taking the marginal power spectrum as its Fourier hologram, the power spectrum at the aperture plane related to its zeroth-order, and its twin images determined by the hermiticity of the cross-spectral density at aperture plane. After realizing that spatial coherence wavelets can be regarded as Wigner distribution functions with similar morphology to the hologram diagrams recently proposed for formulating holography in the phase-space by Lohmann and Testorf, we recognized their power for providing a precise and wide physical interpretation of optical signals in phase space which enables us to apply these holographic features in many fields like optical coherence modulation and beam shaping.

The method of autocorrelation low coherence interferometry is proposed for diagnostics of layered media inner structure. The possible applications of this method in technology and biomedicine are presented. In this method the low coherence optical field is reflected from the object's structure and then analyzed using the Michelson interferometer. Since the object is outside of the Michelson interferometer the axial position of the object is not important and thus the object can move during the measurements. The theoretical background of this autocorrelation method for a media with discrete and continuous optical structure modification is presented.

We use the projected fringes technique to follow the changes induced in the topography of metallic sample sheets subjected to uniaxial tensile tests. Since in-plane strains are associated with out-of-plane deformations, the monitoring of thickness variation of the tensile specimens can be used to detect necking and shear band formation. A sequence of images of the fringe pattern was captured and processed by means of the Fourier transform technique. We measured the material behavior in the elastic and plastic zones during its elongation until fracture took place. We present experimental results for stainless and hot rolled steel sheets.

In this work we present results of measuring deformations on cylindrical objects. The proposed technique is based on panoramic vision principles with convex mirrors, particularly paraboloid mirrors. ESPI techniques are then combined with this panoramic vision system to create a technique suitable of being applied on cylindrical objects. Some results obtained with first-approach mirrors are shown. The system is composed of two modules, illumination and capture, each one needs a paraboloid mirror. Nevertheless this is not the only possible setup when using convex mirrors, an alternative setup is also proposed but is not studied experimentally. Results show the feasibility of the system to determine full-field deformations inside a cylindrical object. The systems is currently being patented and points to an attractive solution in cylindrical or panoramic geometries.