We define the displacement, smear, and jitter components of image motion and derive the two-dimensional statistical image motion optical transfer function (OTF) corresponding to each component. These statistical OTFs are parameterized by means and covariances, which are computed most conveniently from a weighted power spectrum of the line-of-sight motion. Another feature of these results is the realization that all temporal and spatial frequencies contribute to each statistical OTF and that one can determine the frequencies that contribute most significantly to each OTF. Additionally, optical system design is typically based upon the properties of an individual image. In a comprehensive optical system design, the statistical properties of an ensemble of images should also be considered. For individual images subject to a constant but possibly unknown smear length, the OTF is a sinc function. This is called a deterministic smear OTF because it does not describe the smear statistically. The statistical smear OTF describes the average smear OTF for an ensemble of images.
POINTS (Precision Optical INTerferometer in Space) would perform microarcsecond optical astrometric measurements from space, yielding submicroarcsecond astrometric results from the mission. It comprises a pair of independent Michelson stellar interferometers and a laser metrology system that measures both the critical starlight paths and the angle between the baselines. The instrument has two baselines of 2 m, each with two subapertures of 35 cm; by articulating the angle between the baselines, it observes targets separated by 87 to 93 deg. POINTS does global astrometry, i.e., it measures widely separated targets, which yields closure calibration, numerous bright reference stars, and absolute parallax. Simplicity, stability, and the mitigation of systematic error are the central design themes. The instrument has only three moving-part mechanisms, and only one of these must move with sub-milliradian precision; and other two can tolerate a precision of several tenths of a degree. Optical surfaces preceding the beamsplitter or its fold flat are interferometrically critical; on each side of the interferometer, there are only three such. Thus, light loss and wavefront distortion are minimized. POINTS represents a minimalistic design developed ab initio for space. Since it is intended for astrometry, and therefore does not require the u-v-plane coverage of an imaging instrument, each interferometer need have only two subapertures. The design relies on articulation of the angle between the interferometers and body pointing to select targets; the observations are restricted to the `instrument plane.' That plane, which is fixed in the pointed instrument, is defined by the sensitive direction for the two interferometers. Thus, there is no need for siderostats and moving delay lines, which would have added many precision mechanisms with rolling and sliding parts that would be required to function throughout the mission. Further, there is no need for a third interferometer, as is required when out-of-plane observations are made. An instrument for astrometry, unlike those for imaging, can be compact and yet scientifically productive. The POINTS instrument is compact and therefore requires no deployment of precision structures, has no low-frequency (i.e., under 100 Hz) vibration modes, and is relatively easy to control thermally. Because of its small size and mass, it is easily and quickly repointed between observations. Further, because of the low mass, it can be economically launched into high Earth orbit which, in conjunction with a solar shield, yields nearly unrestricted sky coverage and a stable thermal environment.
Newcomb is a design concept for a low-cost astrometric optical interferometer with nominal single-measurement accuracy of 100 microseconds of arc ((mu) as). In a 30 month mission, it will make scientifically interesting measurements of O-star, RR Lyrae, and Cepheid distances, probe the dark matter in our Galaxy via parallax measurements of K giants in the disk, establish a reference grid with internal consistency better than 50 microsecond(s) , and lay groundwork for the larger optical interferometers that are expected to produce a profusion of scientific results during the next century. With an extended mission life, Newcomb could do a useful preliminary search for other planetary systems.