Four-beam laser interferometry for three-dimensional microscopic coordinate measurement.
We propose a new method for calibrating the three-dimensional (3-D) behavior of a scanning stage. Four laser interferometers are used to determine the position of the corner point of a corner mirror attached to the stage. We calculated the 3-D coordinate of the corner point by using only the length information given by the four laser interferometers; thus a method is realized that is traceable from the practical definition of length and that facilitates the optical alignment that is necessary for the interferometers. We calibrated a commercial 3-D stage by the proposed method with a coordinate accuracy of 20-30 nm.
Proposed fast performance evaluation of an imaging system with a discrete detector array.
This paper proposes a newly developed fast measurement of a modulation transfer function (MTF) optical system inclusive of on-axis and off-axis measurement. First, we discuss how a description of an imager in terms of its optical transfer function is not appropriate for a discrete imaging system when aliasing occurs, since these optical systems transform high spatial frequencies into low frequencies; we then measure how an efficient microscanning method could remove the aliasing effects from assigned telecentric optics and nontelecentric optics. A knife edge function and a slit function as a light source are employed in this measurement. The experiment with the newly designed MTF measurement system synchronizes on-axis and off-axis measurement. In addition, a microscan method with a specially written macro is introduced in this experiment to eliminate aliasing effects. After simulation and experimental analysis, first the slit function as a target delivers decent MTF repeatability for this newly developed MTF measurement system, which synchronizes with on-axis and off-axis measurement simply in 2 s after all equipment is ready and aligned. Second, after the six-step microscanning, aliasing will be eliminated to near zero in most cases. Finally, it is concluded that during the microscan, there is no difference between telecentric and nontelecentric optics.
Absolute Measurement of the (220) Lattice Plane Spacing in a Silicon Crystal
The (220) lattice plane spacing of an almost perfect crystal of silicon was measured by means of a combined scanning ($\mathrm{LLL}$) x-ray interferometer and a two-beam optical interferometer. From 170 measurements, a value ${d}_{220}=(192015.560\ifmmode\pm\else\textpm\fi{}0.012)$ fm results in vacuum at 22.50\ifmmode^\circ\else\textdegree\fi{}C. This value is smaller by $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{d}_{220}$ than that reported by Deslattes et al. for another crystal. Generic variabilities of the two crystals account only for a part of this difference.