This PDF file contains the front matter associated with SPIE Proceedings Volume 8133, including the Title Page, Copyright information, Table of Contents, and Conference Committee listing.

For an ordinary laser with two cavity mirrors, if the length of laser cavity changes half wavelength the laser frequency changes one longitudinal mode separation. For a laser with three cavity mirrors, in which a feedback mirror is used to feed part of the laser output beam back into the laser cavity, the external cavity length changes half wavelength the laser intensity fluctuates one period. This presentation gives some research results in measurement field based on changing (tuning) the length of laser internal/external cavity, including 1) HeNe laser cavity-tuning nanometer displacement measurement instruments (laser nanometer rulers), 2) HeNe laser feedback displacement measurement, 3) Nd:YAG laser feedback nanometer displacement measurement, 4) benchmark of waveplate phase retardation measurement based on laser frequency splitting, 5) in-site waveplate phase retardation measurement instruments based on laser feedback and polarization hopping, 6) quasi-common-path microchip Nd:YAG laser feedback interferometer, 7) non-contact Nd:YAG laser feedback surface profile measurement. Some of these instruments have been put into application and display some irreplaceable advantages.

This paper describes a compact, imaging Twyman-Green interferometer to measure small features such as corrosion pits, scratches and digs on hard to access objects such as assembled parts. The shoebox size interferometer was designed to guarantee proper orientation and working distance relative to the inspected section. The system also provides an extended acceptance angle to permit the collection at selected view points on a subject. We will describe the various image shifting techniques investigated as part of the prototype. All the components with the exception of power supplies were integrated into an enclosure. The interferometer has been demonstrated to provide sub-micron depth resolution and diffraction limited spatial resolution (a few microns). This paper will present the final performance achieved with the system and provide examples of applications.

Three-dimensional shape metrology using fringe projection technique and fringe reflection technique are effective ways to reconstruct three-dimensional shape for surfaces with different reflectance properties. Fringe projection technique is used for measuring objects with diffuse surfaces and relies on the principle of triangulation, while fringe reflectometry is used for specular reflective specimens based on principle of reflection. While fringe projection directly provides the profile, fringe reflectometry measures the slope of the surface from which the profile is integrated. In this study, the performance of these two fringe based techniques are investigated in relation to sensitivity and accuracy.

Automatically adapting the camera exposure time is crucial for industrial applications where minimum human intervention is usually desirable. However, it is very challenging to realize such a capability for a conventional fringe projection system where only a finite increment of the exposure time is allowed due to its digital fringe generation nature. Our recent study on generating sinusoidal fringe patterns by properly defocusing binary ones permits the use of an arbitrary exposure time. This provides the potential to adapt the exposure time automatically. This paper will present the principle of an automatic exposure technique and show some experimental results.

A phase reconstruction method using frequency-shifting is proposed. The frequency-shifting method is developed based on the properties of trigonometric functions. The computer simulation and the experimental result are also presented to demonstrate the feasibility and validity of the proposed approach in phase reconstruction.

Solid state light sources are replacing a tungsten filament based bulbs in Scanning White Light Interferometers. White LEDs generate little heat, feature short switching times, and have long lifetimes. Phosphor-based white LEDs produce a wide spectrum but have two separate peaks which cause interferogram ringing. This makes measuring multi layered structures difficult and may degrade measurement precision even when measuring a single reflecting surface. Most non phosphor white LEDs exhibit a non Gaussian spectrum, but multi-LED based white LEDs can achieve switching times and stability similar to those of single color LEDs. By combining several LEDs and by controlling their input current independently it is possible to create almost an arbitrary spectrum. We designed a new light source by combining a non phosphor white LED (American Opto Plus LED, L-513NPWC- 15D) and single color LEDs. This allowed us to fill the spectral gap between the blue and yellow peaks of the non phosphor white LED. By controlling the input current of the LEDs individually a nearly Gaussian shaped spectrum was achieved. This wide continuous spectrum creates short interferograms (FWHM ~1.4 μm) without side peaks. To demonstrate the properties of this source we measured through a 5 μm thick polymer film. The well localized interference created by the source allows measuring both surfaces of thin films simultaneously. We were able to pulse the source at 5.4 MHz.

Three-dimensional measurement based on a pattern projection method has a lot of requirements such as inspections, evaluations and designings in the fields of industry. We have proposed a projection technique using a single MEMS mirror and a laser diode to realize a compact camera for three-dimensional measurement. This projection technique is able to be transformed the mechanism of the projection from time domain to spatial domain. From this technique, we achieved to develop a palm-top camera for three-dimensional profile measurement. In this paper, we propose recent improvement of the principle and its applications. We have developed three-dimensional measurement method based on a single MEMS mirror using three-color laser diodes and 3CCD camera. The measurement method has combined the merits of pattern projection method with the merits of gray code technique.

Triangulation sensors have been in wide use for many years. Most point sensors use a laser spot, which is detected using either a lateral effect photodiode or a linear detector array. The centroid of the spot is used to determine the range using triangulation. On many engineered surfaces, this spot image may suffer from speckle, surface texture, or other issues that limit the ability to repeatably measure the centroid. Many analysis means, such as fitting of the spot, zero crossing, and averaging methods have been tried to make the sensor more robust to surface influenced noise. This paper will present a system using a split image and phase detection to obtain the range. The speed of the sensor is gained by using simple point photodiodes and a moire effect to obtain the phase measurement. The paper will discuss the pros and cons of this approach, and show results on untreated metal parts.ear)

A compact 3-D shape measurement system based on the combined stereovision and phase shifting method has been developed, which consists of a miniature projector and two small cameras arranged as a stereo pair. The projector projects sinusoidal phase shifted fringe patterns, which are captured by both cameras simultaneously. The two phase maps calculated are used for stereo matching. The 3-D shape of the object is then reconstructed by the triangulation method. This research focuses on improving the resolution and accuracy of the measurement system by using a sub-pixel stereo matching method, a multi-image averaging method, and an error compensation method. Experimental results are presented to show the effectiveness of the proposed methods in improving the resolution and accuracy of the system.

It is one of the important necessities to precisely measure the inner diameter and/or the inner profile of pipes, tubes and other objects similar in shape. Especially in mechanical engineering field, there are many requests from automobile industry because the inner surface of engine blocks and other die casts are strongly required to be inspected and measured by non-contact methods (not by the naked eyes inspection using a borescope). If the inner diameter is large enough like water pipes or drain pipes, complicated and large equipment may be applicable. However, small pipes with a diameter ranging from 10mm to 100mm are difficult to be inspected by such a large instrument as is used for sewers inspection. And we have proposed an instrument which has no moving elements such as a rotating mirror or a prism for scanning a beam. Our measurement method is based on optical sectioning using triangulation. This optically sectioned profile of an inner wall of pipe-like objects is analyzed to produce numerical data of inner diameter or profile. Here, we report recent development of the principle and applications of the optical instrument with a simple and compact configuration. In addition to profile measurement, we found flaws and defects on the inner wall were also detected by using the similar principle. Up to now, we have developed probes with the diameter of 8mm to 25mm for small size objects and another probe (80 mm in diameter) for such a larger container with the dimensional size of 600mm.

In this research, we propose to modify a traditional stereo microscope for quantitative 3-D surface profile measurement based on the combined stereovision and phase shifting method. A simple optical system and a miniature projector are used to project phase-shifted fringe patterns to the object surface. Two identical black-and-white cameras are used to capture the fringe images of the object surface, one for each optical channel of the stereo microscope. The calculated phase maps are used for stereo matching at the sub-pixel level. The 3-D surface profile is reconstructed using the triangulation method. Experimental results are presented to demonstrate the feasibility of the proposed method.

Three dimensional, optical measurement systems are becoming more widely used in applications ranging from aerospace to automotive. These systems offer the potential for high speed, good accuracy, and more complete information than older contact based technology. However, the primary standards employed by many to evaluate these systems were specifically designed around touch probe based coordinate measurement machines (CMMs). These standards were designed to work with the limitations of touch probes, and in many cases cannot measure the types of features and errors associated with non-contact systems. This paper will discuss the deficiencies of employing contact based characterization tests to non-contact systems, and suggest a new set of tests specifically to cover the many aspects pertinent to non-contact, optical 3D measurement systems. Some of the performance aspects addressed in this characterization method include: sensitivity to surface reflectivity and roughness, the effect of angle of incidence of measurements, means to characterize volumetric variations that may fit complex functions, and considerations of both spatial and depth resolutions. Specific application areas will be discussed as well as the use of artifacts to provide practical functional data that can predict system performance on real world parts.

A new instrument for measurements of thin transparent flats incorporates a novel in-line normal-incidence equal path interferometer, and extended broad-band illumination to isolate the surface of interest while reducing coherent noise and artifacts. Incorporating a 4Mpix camera, matching high resolution imaging system and vibration robust design; the instrument satisfies the needs of current and future hard disk and pellicle metrology.

3D Non-contact Inspection systems are becoming more capable and affordable, however successful application to complex parts requires understanding the remaining system limitations. Turbine airfoils are key components used in several important industries that present some unique challenges to any metrology application. Issues such as surface finish, complicated shapes and unique geometries exercise many of the key capabilities of a non-contact 3D measurement system. Therefore, many of the short comings of any 3D method become evident in addressing airfoil measurement applications. This paper will address the key challenges posed by complicated shapes such as airfoils, and what gaps still exist in the application of the technology.

In a project to meet requirements for CBP Laboratory analysis of footwear under the Harmonized Tariff Schedule of the United States (HTSUS), a hybrid metrology system comprising both optical and touch probe devices has been assembled. A unique requirement must be met: To identify the interface-typically obscured in samples of concern-of the "external surface area upper" (ESAU) and the sole without physically destroying the sample. The sample outer surface is determined by discrete point cloud coordinates obtained using laser scanner optical measurements. Measurements from the optically inaccessible insole region are obtained using a coordinate measuring machine (CMM). That surface similarly is defined by point cloud data. Mathematically, the individual CMM and scanner data sets are transformed into a single, common reference frame. Custom software then fits a polynomial surface to the insole data and extends it to intersect the mesh fitted to the outer surface point cloud. This line of intersection defines the required ESAU boundary, thus permitting further fractional area calculations to determine the percentage of materials present. With a draft method in place, and first-level method validation underway, we examine the transformation of the two dissimilar data sets into the single, common reference frame. We also will consider the six previously-identified potential error factors versus the method process. This paper reports our on-going work and discusses our findings to date.

The anterior refracting surface of the eye when wearing a contact lens is the thin fluid layer that forms on the surface of the contact lens. Under normal conditions, this fluid layer is less than 10 microns thick. The fluid layer thickness and topography change over time and are affected by the material properties of the contact lens, and may affect vision quality and comfort. An in vitro method of characterizing dynamic fluid layers applied to contact lenses mounted on mechanical substrates has been developed using a phase-shifting Twyman-Green interferometer. This interferometer continuously measures light reflected from the surface of the fluid layer, allowing precision analysis of the dynamic fluid layer. Movies showing this fluid layer behavior can be generated. The fluid behavior on the contact lens surface is measured, allowing quantitative analysis beyond what typical contact angle or visual inspection methods provide. The interferometer system has measured the formation and break up of fluid layers. Different fluid and contact lens material combinations have been used, and significant fluid layer properties have been observed in some cases. The interferometer is capable of identifying features in the fluid layer less than a micron in depth with a spatial resolution of about ten microns. An area on the contact lens approximately 6 mm wide can be measured with the system. This paper will discuss the interferometer design and analysis methods used. Measurement results of different material and fluid combinations are presented.

Conventional methods to measure the positions of the front and rear surfaces of thin films with multiplewavelength interferometers are reviewed to make it clear how the method proposed here is novel and simple. Characteristics of the linear wavenumber-scanning interferometry used in the proposed method are analyzed in detail to make the measurement accuracy clearly. The positions of the front and rear surfaces of a silicon dioxide film with 4μm thickness is measured by utilizing the phases of the sinusoidal waves forms corresponding to each of the optical path differences contained in the interference signal. The experiments and the theoretical analysis show that the measurement error is about 15 nm.

Optical metrology techniques have been widely used in geometric dimension and shape measurements due to many features such as non-contact measurement, fast measurement speed, digital data format for computerized analysis and visualization, superior resolution, and high accuracy, etc. Among these techniques, phase-shifting based surface profilers have drawn more and more attention due to its full-field measurement and maturing wrapping/unwrapping analysis characteristics. This paper analyzes the error sources in phase-shifting surface profilers, including phaseshifting generation, non-linearity compensation, phase-shifting algorithms, surface contour extraction, modeling, and calibration, etc. Some methods to improve the measurement accuracy through coordinate error compensation are also proposed including transfer functions and look-up table (LUT) methods.

Our recent study showed that the phase error caused by improperly defocused binary structured patterns has a unique relationship with the depth z. Based on this finding, the depth information can be extracted without the need of triangulation. Because the measurement can be performed from the same viewing angle, this uniaxial measurement technique can overcome some limitations of a triangulation-based technique, such as measuring a deep hole. This paper will present the principle of the proposed technique and show some simulation and preliminary experimental results to verify its viability.

Two completely localized algorithms for deblurring shift-variant defocused images are presented. The algorithms exploit limited support domain of 2D shift-variant point spread functions (PSFs) to localize the deblurring process. Focused image at each pixel is modeled by a truncated Taylor-series polynomial and a localized equation is obtained which expresses the blurred image as a function of the focused image and its derivatives. This localized equation forms the basis of the two algorithms. The first algorithm iteratively improves the estimated focused image by directly evaluating the localized equation for a given blurred image. The second algorithm uses the localized equation in a gradient descent method to improve the focused image estimate. The algorithms use spatial derivatives of the estimate and hence exploit smoothness to reduce computation. However, no assumptions about the blurring PSFs such as circular symmetry or separability are required for computational efficiency. Due to complete localization, the algorithms are fully parallel, that is, focused image estimates at each pixel can be computed independently. Performance of the algorithms is compared quantitatively with other shift-variant image restoration techniques, both for computational efficiency and for robustness against noise. The new algorithms are found to be faster and do not produce any blocking artifacts that are present in sectioning methods for image restoration. Further, the algorithms are stable and work satisfactorily even in the presence of large blur. Simulation results of the algorithms are presented for both Cylindrical and Gaussian PSFs. The performance of the algorithms on real data is discussed.

Laser triangulation sensors offer a simple, non-contact and fast solution to measure displacement, position, vibration and thickness. However, these sensors are prone to target surface sensitivity since they rely heavily on a uniform back-scatter of the laser spot. Here, sources of measurement noise including surface texture, speckle, beam deflection and asymmetry are discussed. In addition, a few solutions using dithering as well as the beam shaping to reduce surface sensitivity are explored. It is shown that a simple ditherer would induce additional error and a solution is suggested to compensate for it.

In this paper, the design and evaluation of a 3D stereo, near infrared (IR), defect mapping system for CZT inspection is described. This system provides rapid acquisition and data analysis that result in detailed mapping of CZT crystal defects across the area of wafers up to 100 millimeter diameter and through thicknesses of up to 20 millimeter. In this paper, system characterization has been performed including a close evaluation of the bright field and dark field illumination configurations for both wafer-scale and tile-scale inspection. A comparison of microscope image and IR image for the same sample is performed. As a result, the IR inspection system has successfully demonstrated the capability of detecting and localizing inclusions within minutes for a whole CZT wafer. Important information is provided for selecting defect free areas out of a wafer and thereby ensuring the quality of the tile. This system would support the CZT wafer dicing and assembly techniques that enable the economical production of CZT detectors. This capability can improve the yield and reduce the cost of the thick detector devices that are rarely produced today.

Optical shearography techniques were used for the first time to measure the surface resistivity/conductivity of different organic-thin films. Different organic coatings i.e., ACE Premium- gray, white, and beige Enamels (spray coatings), on a metallic alloy, i.e., a carbon steel, were investigated at a temperature range simulating the severe weather temperatures in Kuwait, especially between the daylight and the night time temperatures, 20-60 °C. The investigation focused on determining the in-plane displacement of the coatings, which amounts to the thermal deformation (strain) with respect to the applied temperature range. Then, the alternating current (AC) impedance (resistance) of the coated samples was determined by the technique of electrochemical impedance spectroscopy (EIS) in 3.5 % NaCl solution at room temperature. In addition, a mathematical model was derived in order to correlate between the AC impedance (resistance) and to the surface (in-plane) displacement of the samples in solutions. In other words, a proportionality constant (surface resistivity or conductivity=1/ surface resistivity) between the determined AC impedance (by EIS technique) and the in-plane displacement (by the optical interferometry techniques) was obtained. Consequently the surface resistivity (ρ) and conductivity (σ) of the coated samples in solutions were obtained. Also, electrical resistivity values (ρ) from other source were used for comparison with the calculated values of this investigation. This study revealed that the measured values of the resistivity for the ACE Premium - gray, white, and beige coatings were carried out for the first time. No data on the values of (ρ) were found in literature for the same coatings, using direct current (DC) methods. However, the value range of (ρ) of all investigated coatings, 0.25×10⁸ - 0.27×10¹⁰ Ω-cm was found in the insulator range.

Electronic speckle pattern interferometry is a useful deformation measurement method. In this paper, new method that can measure the deformation by limited information without using much higher speed cameras is proposed. The optical system that can record some spatial information into each speckle of speckle pattern is set up by using basic characteristics of speckle that has never been used before. In experimental results, it is confirmed that the out-of-plane deformation measurement by using only two speckle patterns before and after the deformation can be precisely performed by this method and that the resolution-power of new method is almost equivalent to that of ordinary method.

A novel measurement of laser coarse-fine coupling tracking is proposed for robot trajectory errors, which can not only meet the requirements of large range, rapid response and dynamic tracking, but also achieve the high accuracy of submicroradian magnitude. The mathematic model of robot parameters is deduced according to the motion definition. An experiment platform together with the test system is built to complete the robot trajectory test. The circular and linear trajectory, as well as the harmonious motion parameters, is tested respectively. Some error factors affecting the test uncertainty are given to be considered according to the test experiment results.

We described a multi-probe system comprising three laser interferometers and one autocollimator to measure a flat bar mirror profile with nanometer accuracy. The simulation and pre-experiment of multi-probe system have been conducted on an X-Y linear stage which is composed of a ball bearing slider and a stepping motor. The two standard deviation of the flat bar mirror profile is mainly fitting the range of simulation results (±20 nm). Comparison of our measured data with the results measured by ZYGO white light interferometer system showed agreement to within approximately ±30 nm, excluding some points at the edge of the mirror. From the pre-experiment results, we conclude that the systematic error caused by accuracy of the moving stage can't be ignored. To eliminate this systematic error, the multi-probe system has been implemented on a high-precision micro-coordinate measuring machine (M-CMM) that has been built at the Advanced Industrial Science and Technology (AIST).

An improved arterial pulsation measurement (APM) system that uses three LED light sources and a CCD image sensor to measure pulse waveforms of artery is presented. The relative variations of the pulses at three measurement points near wrist joints can be determined by the APM system simultaneously. The height of the arterial pulsations measured by the APM system achieves a resolution of better than 2 μm. These pulsations contain useful information that can be used as diagnostic references in the traditional Chinese medicine (TCM) in the future.

A new apparatus for blind-guide is proposed in this paper. Optical triangulation method was used to realize the system. The main components comprise a notebook computer, a camera and two laser modules. One laser module emits a light line beam on the vertical axis. Another laser module emits a light line beam on the tilt horizontal axis. The track of the light line beam on the ground or on the object is captured by the camera, and the image is sent to the notebook computer for calculation. The system can calculate the object width and the distance between the object and the blind in terms of the light line positions on the image. Based on the experiment, the distance between the test object and the blind can be measured with a standard deviation of less than 3% within the range of 60 to 150 cm. The test object width can be measured with a standard deviation of less than 1% within the range of 60 to 150 cm. For saving the power consumption, the laser modules are switched on/off with a trigger pulse. And for reducing the complex computation, the two laser modules are switched on alternately. Besides this, a band pass filter is used to filter out the signal except the specific laser light, which can increase the signal to noise ratio.

Recently, an automatic system for grading appearance retention in carpets using our own scanner and image analysis techniques was proposed. A system for carpets with low pile construction and without color patterns has been developed. Appearance changes in carpets with high pile construction were still not well detected. We present an approach based on surface metrology that extract information given by the hairs on the carpet surface. These features are complementary to the texture features previously explored. By combining both features, we expand the use of the automatic grading system including some carpets types with high pile construction.

Due to non-destructive optical techniques allows surface measurement with high accuracy, a Common Path interferometer based on a Michelson configuration was implemented to analyze phase objects by using polarization simultaneous phase-shifting interferometry. Each beam of the interferometer has a birefringent wave plate attached in order to achieve nearly circular polarization of opposite rotations one respect to the other. The system is coupled to a 4-f arrangement with Bi-Ronchi gratings collocated in the Fourier plane. The interference of the fields associated with replicated beams, centered on each diffraction orders, is achieved varying the beams spacing with respect to the grating period. The optical configuration allows obtaining n-interferograms simultaneously. The phase reconstruction is performing by a three steps phase shifting algorithm. Experimental results are present for a phase object.

This paper presents an optical fiber Mach-Zehnder interferometer configured as an ultra-sensitive sound detector. We used a 633nm, 0.5 mW, He-Ne laser, two 3dB couplers, a few meter of telecomm fiber, an U-bench mount to increase the sensitivity of the device and an acquisition system composed by a photodiode and an amplifier connected to a laptop and to an oscilloscope. The optoelectronic device enables us to record acoustic signals from sources at distances longer than 4 meters, converting the interference patterns induced by the sound waves into a digital signal. The ease of its applicability, thanks to its small size and low weight, and its ultra-sensitivity makes this laser microphone a very attractive solution to issues such as monitoring, no-detectable sensing and perimeter protection.

Chip sorter is one of packaging facilities in chip manufactory. Defects will occur for a few of chips during manufacturing processes. If the size of chip defects is larger than a criterion of impacting chip quality, these flawed chips have to be detected and removed. Defects inspection system is usually developed with frame CCD imagers. There're some drawbacks for this system, such as mechanism of pause type for image acquisition, complicated acquisition control, easy damage for moving components, etc. And acquired images per chip have to be processed in radiometry and geometry and then pieced together before inspection. These processes impact the accuracy and efficiency of defects inspection. So approaches of image acquisition system and its opto-mechanical module will be critical for inspection system. In this article, design and characterization of a new image acquisition system and its opto-mechanical module are presented. Defects with size of greater than 15μm have to be inspected. Inspection performance shall be greater than 0.6 m/sec. Thus image acquisition system shall have the characteristics of having (1) the resolution of 5μm and 10μm for optical lens and linear CCD imager respectively; (2) the lens magnification of 2; (3) the line rate of greater than 120 kHz for imager output. The design of structure and outlines for new system and module are also described in this work. Proposed system has advantages of such as transporting chips in constant speed to acquire images, using one image only per chip for inspection, no image-mosaic process, simplifying the control of image acquisition. And the inspection efficiency and accuracy will be substantially improved.

Quasi-monochromatic light reflected from an optically rough surface produces a complicated 3D speckle field. This speckle field is often described using a correlation function from which the 3D speckle properties can be examined. The derivation of the correlation function is based on a physical model where several critical assumptions about the input and output fields in the model are made. However, experimental works verifying this correlation function are rare and sometimes produce inconsistent results. In this paper, we examine some practical issues encountered when experimentally measuring this correlation function, including: The realization of the ensemble average between speckle fields at two point positions; and, The pixel integrating effect of the recording camera and the implications this has for the statistics of the measured speckle field. Following verification of the correlation function and examining the speckle decorrelation properties in 3D space, two practical applications are proposed, one is the aligning of the system optical axis with the camera center and the other is the measurement of the out-of-plane displacement of an object surface. Simulation and experimental results that support our analysis are presented.

Micro-thin wires are of significant importance to academia, research laboratories as well as industries engaged in micro-fabrication of products related to diverse fields like micromechanics, bio-instrumentation, optoelectronics etc. Critical dimension metrology of such wires often demands diameter estimation with tight tolerances. Amongst other measurement techniques, Optical Diffractometry under Fraunhofer approximation has emerged over years as a nondestructive, robust and precise technique for on-line diameter estimation of thin wires. However, it is observed that existing Fraunhofer models invariably result in experimental overestimation of wire diameter, leading to unacceptable error performances particularly for diameters below 50 μm. In this paper, a novel diffraction model based on Geometric theory is proposed and demonstrated to theoretically quantify this diameter overestimation. The proposed model utilizes hitherto unused paths-ways for the two lateral rays that contribute to the first diffraction minimum. Based the 3-D geometry of the suggested model, a new 'diffraction formulation' is proposed. The theoretical analysis reveals the following. For diffraction experiment, the Actual diameter of the diffracting wire is a function of four parameters: source wavelength 'λ', axial distance 'z', diffraction angle corresponding to first diffraction minimum 'θd' and a newly defined characteristic parameter 'm'. The analysis reveals further that the proposed characteristic parameter 'm' varies non-linearly with diameter and presents a dependence only on the experimentally measured diffraction angle 'θd'. Based on the proposed model, the communication reports for the first time, a novel diameter-inversion procedure which, not only corrects for the overestimated but also facilitates wire diameter-inversion with high resolution. Micro-thin metallic wires having diameters spanning the range 1-50 μm are examined. Experimental results are obtained that corroborate the theoretical approach.

Wavelength scanning interferometry based on a reflectometry model is proposed for measuring the absolute thickness profile of a thin silicon wafer. A Fourier-based method of wavelength scanning interferometry is limited to thicker wafers because of a tuning range limitation of the source. As an example, the minimum thickness measurable with the conventional Fourier-based technique using a 4 nm-tunable (500 GHz) 1550 nm laser is approximately 170 μm. Our proposed method enables an extension of thickness measurements with a reduction in systematic measurement error, representing a significant advance. The so-called 'ripple-error' or 'fringe-bleed through' is much lower with a reflectometry-based analysis compared to a Fourier-based analysis. Our method was verified by measuring and testing several wafers with various thicknesses.