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PubMed2003

High-speed path-length scanning with a multiple-pass cavity delay line.

Techniques for high-speed delay scanning are important for low-coherence interferometry, optical coherence tomography, pump probe measurements, and other applications. We demonstrate a novel scanning delay line using a multiple-pass cavity. Differential delays are accumulated with each pass so that millimeter delays can be generated with tens of micrometer mirror displacements. With special design criteria, misalignment sensitivity can be dramatically reduced. The system is demonstrated to scan 6 m/s at 2-kHz repetition rates. Real-time optical coherence tomography imaging with 500 pixel images at four frames/s is performed. Using a Cr:forsterite laser source, we obtained axial image resolutions of 6 microm with 92-dB sensitivity.

Models, Theoretical↗
PubMed2003

Fringe pattern analysis with a parametric method for measurement of absolute distance by a frequency-modulated continuous optical wave technique.

Interferometry associated with an external cavity laser of long coherence length and broad wavelength tuning range shows promising features for use in measurement of absolute distance. As far as we know, the processing of the interferometric signals has until now been performed by Fourier analysis or fringe counting. Here we report on the use of an autoregressive model to determine fringe pattern frequencies. This concept was applied to an interferometric device fed by a continuously tunable external-cavity laser diode operating at a central wavelength near 1.5 microm. A standard uncertainty of 4 x 10(-5) without averaging at a distance of 4.7 m was obtained.

Journal Article↗
PubMed2003

Deep nulling by means of multiple-beam recombination.

Direct detection of exoplanets is possible by use of a technique called nulling interferometry, which is based on destructive interference of light of the bright object and constructive interference of the faint object. In the infrared wavelength region, this implies that light of a star must be attenuated by a certain factor, the so-called rejection ratio, which typically equals 10(6). This can be achieved by use of phase shifters, which apply a phase shift of pi rad with an average error nogreater than 2 mradover a predefined wavelength region. For a 6-18-microm wavelength interval, this is a tough constraint. We show that the 2-mrad constraint can be relaxed if more than two beams participate in the beam recombination. We focus our attention on dispersive phase shifters and show that rejection ratios beyond 10(6) can be reached easily by use of a system of four or more apertures and simple dispersive phase shifters that consist of only one material.

Journal Article↗
PubMed2003

Measuring temperature profiles in high-power optical fiber components.

We demonstrate a new method for measuring changes in temperature distribution caused by coupling a high-power laser beam into an optical fiber and by splicing two fibers. The measurement technique is based on interrogating a fiber Bragg grating by using low-coherence spectral interferometry. A large temperature change is found owing to coupling of a high-power laser into a multimode fiber and to splicing of two multimode fibers. Measurement of the temperature profile rather than the average temperature along the grating allows study of the cause of fiber heating. The new measurement technique enables us to monitor in real time the temperature profile in a fiber without the affecting system operation, and it might be important for developing and improving the reliability of high-power fiber components.

Journal Article↗
PubMed2003

Miniaturized digital holography sensor for distal three-dimensional endoscopy.

A miniaturized sensor head for endoscopic measurements based on digital holography is described. The system was developed to measure the shape and the three-dimensional deformation of objects located at places to which there is no access by common measurement systems. A miniaturized optical sensor, including a complete digital holographic interferometer with a CCD camera, is placed at the end of a flexible endoscope. The diameter of the head is smaller than 10 mm. The system enables interferometric measurements to be made at speeds of as many as five reconstructions per second, and it can be used outside the laboratory under normal environmental conditions. Shape measurements are performed with two wavelengths for contouring, and the deformation is measured by digital holographic interferometry. To obtain full three-dimensional data in displacement measurements we illuminate the object sequentially from three different illumination directions. To increase the lateral resolution we use temporal phase shifting.

Endoscopes↗
PubMed2003

Direct writing of microlenses in polycarbonate with excimer laser ablation.

A method for fabricating microlenses in polycarbonate material is reported. Using a direct-write technique based on scanning excimer laser ablation with a circular beam, we can etch an arbitrary shape in the polymer material. The beam is obtained by imaging a circular aperture onto the polymer surface, and scanning is realized by the translation stage carrying the sample, which makes successive contours with well-chosen diameters and scan velocities. Afterward, to smooth the ablated surface and release it from debris, a large beam aperture covering the full lens area is used to ablate the lens deeper into the substrate. The fabrication process and the characterization method are described, including calculation of the contour set for a desired lens shape. The optical performance is evaluated by Mach-Zehnder interferometry, showing that aberrations below lambda/10 are possible for slow lenses.

Journal Article↗
PubMed2003

Phase-shifting with computer-generated holograms written on a spatial light modulator.

We propose a new computer-controlled phase-shifting method based on computer-generated holograms (CGHs) displayed on a spatial light modulator (SLM). In this method the accurate phase shifts required in phase-shifting digital holography or interferometry are induced by a suitable transformation of the encoding patterns of the CGH displayed on a SLM. Both the theoretical analysis and the experimental results demonstrate the feasibility of this approach. We also discuss possible applications of this method in the field of interferometric null testing of aspheres.

Journal Article↗
PubMed2004

Three-dimensional object feature extraction and classification with computational holographic imaging.

We address three-dimensional (3D) object classification with computational holographic imaging. A 3D object can be reconstructed at different planes by use of a single hologram. We apply principal component and Fisher linear discriminant analyses based on Gabor-wavelet feature vectors to classify 3D objects measured by digital interferometry. Experimental and simulation results are presented for regional filtering concentrated at specific positions and for overall grid filtering. The proposed technique substantially reduces the dimensionality of the 3D classification problem. To the best of our knowledge, this is the first report on the use of the proposed technique for 3D object classification.

Journal Article↗
PubMed2004

Moiré interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms.

We present a procedure using continuous wavelet transforms (CWTs) to extract the phase information from moiré interferograms. The relationship between precise ridge detection of the two-dimensional CWT magnitude map and accurate phase extraction is detailed. A cost function is introduced for the adaptive selection of the ridge, and a computationally inexpensive implementation of the cost function ridge detection algorithm is explored with dynamic programming optimization. The results of the proposed ridge detection algorithm on actual interferograms are illustrated. Moreover, the resulting extracted phase is demonstrated to be smooth and accurate. As a result, the sensitivity of the moiré interferometry method is improved to obtain a pixel-by-pixel in-plane strain distribution map.

Journal Article↗
PubMed2004

Wave-front reconstruction from shear phase maps by use of the discrete Fourier transform.

Fast wave-front reconstruction methods are becoming increasingly important, for example, in large astronomical adaptive optics systems and high spatial resolution shear interferometry, where pseudoinverse matrix methods scale poorly with problem size. Wave-front reconstruction from difference measurements can be achieved by use of fast implementations of the discrete Fourier transform (DFT), obtaining performance comparable with that of the pseudoinverse in terms of the noise propagation coefficient. Existing methods that are based on the use of the DFT give exact results (in the absence of noise) only for the particular case in which the shear is a divisor of the number of samples to be reconstructed. We present two alternate solutions for the more general case when the shear is any integer. In the first solution the dimensions of the problem are enlarged, and in the second the problem is subdivided into a set of smaller problems with shear amplitude equal to one. We also show that the retrieved solutions have minimum norm and calculate the noise propagation coefficient for both methods. The proposed algorithms are implemented and timed against pseudoinverse multiplication. The results show a speed increase by a factor of 50 over the pseudoinverse multiplication for a grid with N = 3 x 10(3) samples.

Journal Article↗
PubMed2004

Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer.

Wavelength-scanning interferometry permits the simultaneous measurement of variations in surface shape and optical thickness of a nearly parallel plate. Interference signals from both surfaces of the test plate can be separated in frequency space; however, these frequencies are shifted from the expected frequency by the refractive-index dispersion of the test plate and any nonlinearity that is due to wavelength scanning. Conventional Fourier analysis is sensitive to this detuning of the signal frequency and suffers from multiple-beam interference noise. We propose new wavelength-scanning algorithms that permit a large tolerance for dispersion of the test plate and nonlinearity of scanning. Two 19-sample algorithms that suppress multiple-interference noise up to the second order of the reflectance of the test plate are presented. Experimental results show that the variation in surface shape and optical thickness of a glass parallel plate of 250-mm diameter was measured with a resolution of 1-2 nm rms.

Journal Article↗
PubMed2004

Step-height measurement by means of a dual-frequency interferometric confocal microscope.

A novel instrument, the dual-frequency interferometric confocal microscope (DICM), which facilitates the measurement of step features, is investigated. It combines the advantages of the high resolution (subnanometer) of heterodyne interferometry and the relatively large measurement range (approximately 5 microm) of confocal microscopy. The axial response curves of the confocal microscopy system are compared in experiments in which microscopic objects with various numerical apertures and magnifications are used. The results prove that the variation in light intensity is enough to permit discrimination of different orders of interference fringes. The DICM has been successfully utilized to measure the step height of a standard mask, and the experimental results agree well with those measured by scanning probe microscopes. The results also show that the system has good repeatability, with a maximum deviation of 5 nm.

Journal Article↗
PubMed2004

Performance evaluation of iterative tomography algorithms for incomplete projection data.

Projection data obtained through optical techniques for tomographic measurements, such as interferometry for refractive-index-based measurements, are often incomplete. This is due to limitations in the optical system, data storage, and alignment and vignette issues. Algebraic iterative reconstruction techniques are usually favored for such incomplete projections. A number of iterative algorithms, based on additive and multiplicative corrections, are used with a known simulated phantom and noise source to assess the reconstruction performance of incomplete data sets. In addition, we present reconstructions using experimental data obtained from a coherent gradient sensing interferometer for a steady temperature field in a fluid medium. We tested the algorithms using the simulated data set for incompleteness conditions similar to those found in the experimental data, and the best-performing algorithm is identified.

Journal Article↗
PubMed2004

Interferometric analysis of nanostructured surface profiles: correcting material-dependent phase shifts.

We present a technique to correct interferometry for the material-dependent phase shift that accompanies reflection. Such corrections are needed for nanometer accuracy of surfaces that are not of homogeneous composition. We adapt the general theory of reflection from surfaces in which there are irregular and unresolved areas of several materials to treat the specific case in which only two materials are present, as is the case for many practical applications. We show, for the approximation of a large numerical aperture that collects all reflected light, how measurements of three quantities, together with known values of the optical constants, allow determination of the material-dependent phase shift at each position on the surface. We demonstrate with numerical simulation, appropriate to measuring a surface of alumina in which optically unresolved titanium carbide granules are embedded, that our approach also succeeds, with nanometer accuracy, when the numerical aperture is small. The method is discussed for use with a miniature interferometric phase sensor, but it has application to any interferometer.

Journal Article↗
PubMed2004

Practical realization of high-speed photodisplacement imaging by use of parallel excitation and parallel heterodyne detection: a numerical study.

A new parallel photodisplacement technique that achieves extremely high-throughput imaging is proposed, and its practical realization is studied numerically. In this technique, a linear region of photothermal displacement is excited by use of a line-focusing intensity-modulated laser beam and detected with a parallel heterodyne interferometer in which a charge-coupled device linear image sensor is used. Because of the integration and sampling effects of the sensor, the interference light is spatiotemporally multiplexed. To extract the photodisplacement component from the multiplexed sensor signal, a scheme of phase-shifting light integration under an undersampling condition is proposed for parallel interferometry. The frequencies of several control signals, including the heterodyne beat signal, modulation signal, and sensor gate signal, are optimized so as to eliminate undesirable components, allowing only the displacement component to be extracted. Preliminary numerical simulation results show that the proposed technique has the potential to perform photodisplacement imaging more than 10,000 times faster than conventional photoacoustic microscopy.

Journal Article↗
PubMed2004

Scattering of light by a periodic structure in the presence of randomness. III. Limit of the extended matched filtering method for the detection of weak periodicities.

It is known that, for scattering of light by a rough grating, the periodically occurring intensity maxima that are characteristic of the periodic part of the scattering medium get smeared off and hence become undetectable if coherence length r0 of the randomness is much smaller than wavelength A of the periodic part of the grating. It is also known that by conventional intensity measurements the detectability region is r0/lambda > or = 0.33, which can be extended to lower regions by intensity interferometry. It is established here that an extended matched filtering method enables one to detect the periodic part of the medium, even in the presence of higher roughness (i.e., lower r0), and the limit is placed at r0/lambda approximately 0.11 by our numerical experiments.

Journal Article↗
PubMed2004

Simple phase-shifting method in a wedge-plate lateral-shearing interferometer.

A simple phase-shifting method in a wedge-plate lateral shearing interferometer is described. Simply moving the wedge plate in an in-plane parallel direction gives the amount of phase shift required for phase-shifting interferometry because the thickness of a wedge plate is not constant and varies along the wedge direction. This method requires only one additional linear translator to move the wedge plate. The required moving distance for a phase shift of the wave front with this method is of the order of a millimeter, whereas the typical moving distance for another method that uses a piezoelectric transducer is of the order of a wavelength. This method yields better precision in controlling the moving distance than do the other methods.

Journal Article↗
PubMed2004

Class of 4 + 1-phase algorithms with error compensation.

It is well known that phase-shifting interferometry suffers from inaccuracy in the presence of phase-shifting errors. We have proved the limitation of using a 4-phase algorithm to reduce the phase-measurement error in the presence of the phase-shifting error. A class of 4 + 1-phase error compensating algorithms is formulated. It is shown that the proposed algorithms can effectively minimize the effects of the constant phase-shifting error and possess a superior performance than existing error-compensating algorithms. The effectiveness of the proposed algorithm is demonstrated by computer simulations and experiments.

Journal Article↗