A time-of-flight measurement-based three-dimensional (3D) profiler system employing a lightweight scanning system is demonstrated. To reduce the weight of the scanning system, and thereby achieve faster scanning speeds, two Fresnel prism sheets were employed as the scanning optics and installed to work as a pair of Risley prisms. Each Fresnel prism sheet has a diameter of 102 mm and mass of 15 g, which is about 12 times lighter than ordinary bulky prism. By scanning the laser beam with the developed scanning system, a 3D point cloud image of a target object located 8 m away could be successfully obtained. The image distortion was removable by correcting six geometrical parameters of the scanner using a simple optimization algorithm. It was confirmed by the experiment that once the distortion has been corrected, it is valid for other scanning speeds (and trajectories), enabling 3D profile measurements that do not require postprocessing of measured data. Measurement results for a standard target composed of square extrusions were in good agreement with the reference values, with deviations of <1 mm.
The uncertainties of measuring the geometrical thickness and refractive index of silicon wafers were evaluated. Both quantities of the geometrical thickness and refractive index were obtained using the previously proposed method based on spectral domain interferometry using the optical comb of a femtosecond pulse laser. The primary uncertainty factor was derived from the determination process of the optical path differences (OPDs) including the phase calculation, measurement repeatability, refractive index of air, and wavelength variation. The uncertainty for the phase calculation contains a Fourier transform in order to obtain the dominant periodic signal as well as an inverse Fourier transform with windowed filtering in order to calculate the phase value of the interference signal. The uncertainty for the measurement repeatability was estimated using the standard deviation of the measured optical path differences. During the experiments, the uncertainty of the refractive index of air should be considered for wavelengths in air because light travels through air. Because the optical path difference was determined based on the wavelength in use, the variation of the wavelength could also contribute to the overall measurement uncertainty. In addition, the uncertainty of the wavelength depends on the wavelength measurement accuracy of the sampling device, i.e. the optical spectrum analyzer. In this paper, the details on the uncertainty components are discussed, and future research for improving the performance of the measurement system is also proposed based on the uncertainty evaluation.
We describe a method to simultaneously measure both thickness profile and refractive index distribution of a silicon wafer based on a lateral scanning of the wafer itself. By using dispersive interferometer principle based on a broadband source, which is a femtosecond pulse laser with 100 nm spectral bandwidth, both thickness profile and refractive index distribution can be measured at the same time using a single scanning operation along a lateral direction. The proposed measurement system was tested using an approximately 90 mm range with a 0.2 mm step along the center-line, except for the rim area in a ϕ100 silicon wafer. As a result, the thickness profile was determined to have a wedge-like shape with an approximately 2 μm difference at an averaged thickness of 478.03 μm. Also, the mean value of the refractive index distribution was 3.603, with an rms value of about 0.001. In addition, the measurement uncertainty of the thickness profile was evaluated by considering two uncertainty components that are related to the scanning operation, like the yaw motion of the motorized stage and the long-term stability of an optical path difference in an air path. The measurement reliability of both the thickness profile and refractive index distribution can be increased through several methods such as an analysis of the correlation between the thickness profile and the refractive index distribution and a comparative measurement using a contact-type method; these potential methods are the subject of our future work.
We report on the calibration results of the wavelength of the lasers used in commercial laser interferometers, including the vacuum wavelength deviation from its nominal value, the vacuum wavelength stability, the repeatability of stabilized wavelength, and the secular change of these properties, by analyzing the calibration data accumulated for more than two decades. We present an experimental method of calibrating the frequency of laser interferometers. We also propose a proper time interval and an appropriate uncertainty expression for the vacuum wavelength calibration of the laser interferometers.
We propose a microscopic system which could be applied to three-dimensional surface profile measurement. In the
system, a two-dimensional pinhole array is imaged onto the surface under measurement by an objective lens. These spots
act as discrete object points which are then imaged to the CCD chip by the microscope which contains two orthogonal
cylindrical lenses. Due to the astigmatism of the two cylindrical lenses, the shape of the image of object points on the
CCD camera becomes oval unless the object point is located at a position which satisfies the best imaging condition. By
calculating the focus error signal using the intensities measured at a group of CCD cells, the information on the distance
of the corresponding object point could be found out.
The basic concept of the system was checked by computer simulation on the point spread function of various object
points. A preliminary measurement system which consists of the same optical components used in the computer
simulation has been set up for verification of the idea. Since this system requires only one image to analyze the surface
profile, it is a one-shot measurement system, and is insensitive to environmental noises such as mechanical vibration.
We developed a gauge block interferometer which utilizes the frequency tunable laser diodes as both light sources and
phase shifters of a phase shifting interferometer. By using a confocal Fabry-Perot cavity made of ultra low expansion
glass, and linearly modulating the laser diode current, the laser frequency could be injection locked to the resonant
modes of the Fabry-Perot cavity consecutively. These equal spaced frequencies produce equally phase shifted
interferometric images which are ideal to be analyzed by the Carré algorithm. Two frequency scanning lasers at the
wavelengths of 636 nm and 657 nm are used as light sources for the gauge block interferometer. The system takes only
10 ms for a single measurement which acquires two sets of four equally phase shifted images with 640×480 pixels in
size. Central lengths of gauge blocks are measured by using the phase shifting interferometry and exact fraction method.
The performance of the high speed interferometer could be checked by comparing the measurement results on the same
gauge block made by two different methods. Two results agreed well within the measurement uncertainty.
A total integrated scattering (TIS) system consisting of an integrating sphere has been developed in KRISS for the
purpose of measuring the effective roughness amplitude of gauge blocks and platens, which are necessary for the
correction of phase shift due to roughness difference between gauge block and platen, in the calibration of gauge blocks
by optical interferometry. Details on the TIS system and its calibration by using two different methods are described. The
uncertainty of the effective roughness amplitude measurement by using the TIS system is evaluated to be 2 nm (k=1).
This paper presents the design and fabrication of a precision dual level stage composing a dimensional metrological
system for large range surface topography, such as mask patterns for lithography, fine artifacts on a semi-conductor
wafer and micro roughness on a large specular surface. The stage was configured as dual level, a fine stage on a coarse
stage, to obtain large moving range and high resolution simultaneously. In the design of the coarse stage, we focused on
a simple structure with low profile to achieve insensitivity to vibration and high accuracy. Therefore, a high quality flat
surface plate was used as the reference plane of the coarse stage's movement, instead of a conventional simple stacking
of two long stroke one-axis stages. The surface plate also has a role of metrological frame for very low thermal
expansion coefficient and its size is 800 mm × 800 mm. The coarse stage is guided horizontally by a cross structure with
two precision straight bars perpendicularly linked and vertically by the surface plate. The sliding pads made of PTFE are
used to guarantee the smooth motion of the coarse stage for both horizontal and vertical directions. The fine stage fixed
on the coarse stage generates five-axis fine motion, such as two-axis in-plane translation, one-axis in-plane and two-axis
out-of-plane rotation. The fine stage is composed of flexure guided structures and actuated by five PZTs. The developed
dual level stage can achieve a large range of 200 mm × 200 mm and a nanometric resolution simultaneously. Its
movement is monitored and controlled using a five-axis laser interferometer system to be applied to a dimensional
metrology having direct meter-traceability.
We report an exploitation of the optical comb of a femtosecond pulse laser as the wavelength ruler for the task of absolute length calibration of gauge blocks. To that end, the optical comb was stabilized to an Rb atomic clock and an optical frequency synthesizer was constructed by tuning an external single-frequency laser to the optical comb. The absolute height of gauge blocks was measured by means of multi-wavelength interferometry using multiple beams of different wavelengths consecutively provided by the optical frequency synthesizer. The wavelength uncertainty was measured 1.9 × 10-10 that leads to an overall calibration uncertainty of 17 nm (k=1) in determining the absolute length of gauge blocks of 25 mm nominal length.
The pitch and orthogonality of two-dimensional (2D) gratings have been calibrated by using an optical diffractometer (OD) and a metrological atomic force microscope (MAFM). Gratings are commonly used as a magnification standard for a scanning probe microscope (SPM) and a scanning electron microscope (SEM). Thus, to establish the meter-traceability in nano-metrology using SPM/SEM, it is important to certify the pitch and orthogonality of 2D gratings accurately. ODs and MAFMs are generally used as effective metrological instruments for the calibration of gratings in nanometer range. Since two methods have different metrological characteristics, they give complementary information for each other. ODs can measure only mean pitch value of grating with very low uncertainty, but MAFMs can obtain individual pitch value and local profile as well as mean pitch value, although they have higher uncertainty. Two kinds of 2D gratings, each with the nominal pitch of 700 nm and 1000 nm, were measured, and the uncertainties of calibrated values were evaluated. We also investigated the contribution of each uncertainty source to the combined standard uncertainty, and discussed the causes of main ones. The expanded uncertainties (k = 2) of calibrated pitch values were less than 0.05 nm and 0.5 nm for the OD and the MAFM, and the calibration results were coincident with each other within the expanded uncertainty of the MAFM.
A compact linear and angular displacement measurement device was developed by combining a Michelson interferometer in Twyman-Green configuration and an autocollimator to characterize the movement of a precision stage. A precision stage usually has 6 degrees of freedom of motion (3 linear and 3 angular displacements) due to the parasitic motions, thus linear and angular displacement should be measured simultaneously for the complete evaluation of precision stage. A Michelson interferometer and an autocollimator are typical devices for measuring linear and angular displacement respectively. By controlling the polarization of reflected beam from the moving mirror of the interferometer, some parts of light are retro-reflected to the light source and the reflected beam can be used for angle measurement. Because the interferometer and the autocollimator have the same optic axis, the linear and angular displacements are measured at the same position of the moving mirror, and the moving mirror can be easily and precisely aligned to be orthogonal to the optic axis by monitoring the autocollimator's signal. A single mode polarization maintaining optical fiber is used to deliver the laser beam to the device, and all components except the moving mirror are fixed with bonding to achieve high thermal and mechanical stability. The autocollimator part was designed to have the angular resolution of 0.1" and the measurement range of 60". The nonlinearity error of interferometer was minimized by trimming the gain and offset of the photodiode signals.
This paper describes a fringe scanning Fourier transform method to automatically measure the fractional interference order in gauge block interferometry. The advantages of the proposed method are presented with the comparison of measurement results between the existing Fourier transform method and the fringe scanning Fourier Transform method. The configuration of automatic gauge block measuring system is also described, where the proposed method is applied. The standard uncertainty evaluation of the fractional interference order measurement with this method is given.
We proposed a novel interferometer, which can measure the 3-dimensional coordinates of freely moving objects in space. The interferometer is composed of two fiber ends and three photo detectors. Frequency stabilized laser is incident into an optical fiber, and then split by the fiber beam splitter into two fiber ends. One fiber is used as the fixed reference arm, and the other as the movable test arm of the interferometer. By using servo control on one arm, the phase difference of the laser beams being emitted from the two fiber ends is forced to be kept constant. Beams from each fiber end are combined at the photo detectors on which interference fringes are formed. The displacement of the distances of the moving fiber end (MFE) from the three detectors can be measured by analyzing the interference fringe. From the measured distances of the MFE from each detector, the 3-dimensional coordinates of the MFE are obtained in real time by using the triangulation. Since the wavefront of the beam from the MFE is spherical, the displacement of the MFE is not restricted to a specific direction, which requires no guiding rail for the moving object. This interferometer could be applied to situations where 3-dimensional coordinates of freely moving objects are being measured with high precision.
Double-ended Fizzeau type interferometers can be applied advantageously for direct dimensional measurements of regular bodies with parallel, flat measuring surfaces. At PTB, such an interferometer with specific equipment for phase stepping interferometry has been developed. The basic interferometer or etalon consists of two parallel, semi- reflecting reference plates. The symmetrical arrangement of two optical systems for illumination and observation of the interference pattern allows alternating measurements from both sides. The interference systems are observed in reflection and focused onto CCD-cameras. The optical pates are attached to a rigid frame, so that both an adjustment of the interference and a parallel displacement for the phase stepping technique is obtained. Servo-control units allow a precise value of 1/4 interference order for the displacement to be adjusted, which is necessary for a special Fizzeau algorithm. The dimensions of the interferometer are designed for volume measurements of cubes of about 80 mm, which are used as density standards. The distance topography between two opposed surfaces of the cubes are derived from measurements of the empty etalon and measurements with the cube inserted. The interferometer can also measure gauge blocks which are not wrung to a base plate by direct optical probing of the free surfaces and explore the influence of roughness and optical phase shift.
We developed a system which can calibrate the vertical magnification of surface roughness testers in the range of Itc, 0.1 ti 10 µm with high accuracy. The system consists of an electromechanical transducer(EMT) and a heterodyne laser interferometer. With voltage applied, EMT simulates a sinusoidal surface and heterodyne laser interferometer is used to measure the amplitude of the simulated surface. By calculating the theoretical roughness value for this surface, and dividing it by the measured roughness value, we can obtain the calibiation constant. With this calibration system, the relative uncertainty of calibration is 2%.
We describe a holographic deformation measurement system which uses FFT and carrier fringe method. Since all processes are fully automatic and we use a real time holographic interferometer, continuous deformation could be measured in real time.
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