There is an increasing need for on-site measurements in the manufacturing industry. In several cases, the shape of a work piece needs to be optically measured in high-temperature atmospheres up to 500 °C. Measurement errors caused by a lump of high-temperature air in an optical path were theoretically investigated using a model of a cylindrical lens made of air. Errors predicted by the model qualitatively explained the experimental results well. Quantitatively, the predicted errors were always larger than the experimental ones. The model was found to be useful for estimating the maximum values of the errors, which has important practical uses.
Bessel beams formed by an axicon are nondiffracting beams. Such beams are used in the field of laser machining because they have several desirable characteristics, including a micron-sized focal spot and a deep focal depth. Conical lenses are generally employed for producing Bessel beams. A binary diffractive axicon was made by electron beam fabrication; the first-order diffracted beam from this axicon has a similar optical field to that of a refracted beam from a conical lens. The characteristics of a laser beam spot focused by the axicon were investigated. We demonstrated theoretically and experimentally that the peak intensity on the optical axis oscillated with a larger amplitude as the spot size decreased when the beam spot was observed in the vicinity of the axicon. This phenomenon was well explained by taking higher-order diffraction into account. We also investigated the wavelength dependence of the spot size focused by the axicon, and found that the spot size was constant.
Liquid crystal spatial light modulators (LCSLMs) are promising devices for real-time holography. We are trying to use a twisted nematic LCSLM as a phase hologram. In previous years, only linearly polarized light has been applied to use the device as a phase-only modulator. Recently, eigenstates of the device were studied using Jones matrix calculus. The eigenvectors of the device represents elliptically polarized light, and the negative eigenvector indicates the preferable performance for phase-only modulation. In this paper, we generalize the calculus by introducing a polar coordinate system and angular parameters. This simplifies the analysis of device characteristics and makes it easier. It also enables us to discuss more precisely the intensity transmission and phase delay caused by the device. Finally, we present the optimum eigenvector for phase modulation in terms of the birefringence range of the LCSLM.
In phase shifting interferometers, spatial non-uniformity of the phase modulation often happens and affects high- precision phase measurement. Many phase measuring algorithms have been reported which compensate for nonlinear sensitivities of the phase shifter. This nonlinearity of the phase shifter usually gives only a constant bias to the measured phase in these algorithms. However, when the phase shift is spatially nonuniform, the measured phase is shown to suffer significant errors from these bias phase. We have shown that if we add a new symmetry to an algorithm we can remove the errors caused by the spatial nonuniformity of the phase shift. The algorithm needs at least one more image frame to acquire the symmetry. The lowest-order algorithm that compensates for a quadratic and spatially nonuniform phase shift consists of six frames. We have compared the performance of the new algorithm on several types of phase nonuniformity to the conventional error-compensating algorithms.
A new method for measuring the straightness of travel of a moving table is described. The method uses two conjugate beams diffracted from a holographic grating that is mounted on the moving table. The intensity of two-beam interference is measured and the transverse displacement of the table is calculated from the change in intensity. The system is theoretically capable of measuring the transverse displacement to nanometer-order accuracy. Experimentally, a transverse displacement measurement with an accuracy of 0.12 μm was obtained over a staged travel of 100 mm.
Fringe counting techniques are often used in modern laser interferometers for measuring displacement. These interferometers are essentially integrating devices, where the displacement is derived from an accumulated fringe count; that is, they measure travel rather than static displacement. If the interferometer optical paths are interrupted during a measurement cycle, the reference for the instrument is lost and accuracy suffers. In this paper, we describe a holographic technique whereby displacement is measured by analyzing a fringe pattern localized at infinity which is equivalent to Haidinger or Brewster fringes in conventional interferometry. The phase distribution of the fringe pattern is measured to high accuracy using phase-stepping interferometry, and then analyzed by computer. Using this technique, we were able to measure in plane displacements with an accuracy of about 0.2 micrometers , while the accuracy for out of plane displacements was about 2 micrometers .
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.