Absolute surface metrology with a phase-shifting interferometer for incommensurate transverse spatial shifts.

We consider the detailed implementation and practical utility of a novel absolute optical metrology scheme recently proposed for use with a phase-shifting interferometer (PSI). This scheme extracts absolute phase differences between points on the surface of the optic under test by differencing phase maps made with slightly different transverse spatial shifts of that optic. These absolute phase (or height) differences, which for single-pixel shifts are automatically obtained in the well-known Hudgin geometry, yield the underlying absolute surface map by standard wavefront reconstruction techniques. The PSI by itself maps surface height only relative to that of a separate reference optic known or assumed to be flat. In practice, even relatively high-quality (and expensive) transmission flats or spheres used to reference a PSI are flat or spherical only to a few dozen nanometers peak to valley (P-V) over typical 4 in. apertures. The new technique for removing the effects of the reference surface is in principle accurate as well as simple, and may represent a significant advance in optical metrology. Here it is shown that transverse shifts need not match the pixel size; somewhat counterintuitively, the single-pixel spatial resolution of the PSI is retained even when transverse shifts are much coarser. Practical considerations for shifts not necessarily commensurate with pixel size, and broader applications, are discussed.

Telescope alignment from sparsely sampled wavefront measurements over pupil subapertures.

We present a simple formalism that has proven useful in on-axis alignment of two-element telescopes when wavefront information is available from only a limited region (here two noncontiguous subapertures) of the pupil. Misalignments cause predictable full-aperture aberrations, which in turn cause predictable tip/tilt modes in the subapertures. For the most useful case in which secondary mirror tilts are independently constrained by optical monitoring, the four subaperture tip/tilt modes provide enough information to solve for the state of misalignment uniquely. A practically important and intuitively appealing simplification of this inversion occurs if the tip/tilts of the two subapertures are first transformed into a new basis consisting of differential and common-mode tilts in each of the x and y directions. Then the matrices interpreting subaperture modes as full-aperture aberrations and those in turn as mechanical misalignments become diagonal, so the mechanical adjustment required to align each degree of freedom is just a constant sensitivity multiplying one of the measured differential or common-mode tilt basis modes. Knowing that this simplification occurs allows rapid empirical calibration of sensitivities in the lab and then deterministic alignment, simply and transparently, with no need for ray tracing to model the optical effects of the adjustments at each step of the alignment.

Absolute surface metrology by differencing spatially shifted maps from a phase-shifting interferometer.

Surface measurements of precision optics are commonly made with commercially available phase-shifting Fizeau interferometers that provide data relative to flat or spherical reference surfaces whose unknown errors are comparable to those of the surface being tested. A number of ingenious techniques provide surface measurements that are "absolute," rather than relative to any reference surface. Generally, these techniques require numerous measurements and the introduction of additional surfaces, but still yield absolute information only along certain lines over the surface of interest. A very simple alternative is presented here, in which no additional optics are required beyond the surface under test and the transmission flat (or sphere) defining the interferometric reference surface. The optic under test is measured in three positions, two of which have small lateral shifts along orthogonal directions, nominally comparable to the transverse spatial resolution of the interferometer. The phase structure in the reference surface then cancels out when these measurements are subtracted in pairs, providing a grid of absolute surface height differences between neighboring resolution elements of the surface under test. The full absolute surface, apart from overall phase and tip/tilt, is then recovered by standard wavefront reconstruction techniques.

Feasibility of symmetry-based speckle noise reduction for faint companion detection.

Great interest has been focused on the problem of detecting faint companions, possibly including extrasolar planets, very close to other stars. A promising approach involves coupling high-correction adaptive optics to coronagraphs, for which many new and innovative designs have emerged. Detection of faint companions will require suppression of noise due to fluctuating speckles from the remnant fraction of stellar light not adaptively controlled. At high correction, the speckle halo takes on distinct spatial symmetries that may allow partial speckle noise reduction through relatively simple post-processing that rejects one spatial symmetry in the image. This paper quantitatively examines potential companion-detection sensitivity improvements that might be expected, and shows that realistic operational parameters will allow them to be realized.

Achromatic four-quadrant phase mask (FQPM) coronagraphy using natural beam splitter phase shifts.

The four-quadrant phase mask (FQPM) is an exciting new approach to coronagraphy, a classic astronomical technique for detecting faint companions very close to bright stars. Starlight rejection is potentially very high, and inner working distances are substantially smaller than those achieved with classical Lyot coronagraphy. The key component of the original FQPM scheme is a transparent mask divided into quadrants delivering relative phase shifts alternately 0/pi/0/pi, inserted in an intermediate focal plane of the telescope. Monochromatic masks of this kind have been successfully demonstrated in laboratory and telescope tests. Fabrication of masks with achromatic pi phase shifts is challenging but of great interest for optimum astronomical sensitivity. In this paper I present a novel concept for achromatic FQPM operation that utilizes intrinsic phase relationships between transmitted and reflected beams in a dielectric beam splitter.

Static point-spread function correction dominating higher-order speckle terms at high adaptive correction.

At high adaptive correction, the randomly shifting speckles familiar in conventional astronomical imaging become organized into patterns with distinct regularities that may permit partial suppression of the image noise they produce. Mathematically, the phase exponential in the Fourier-optical imaging expression may be expanded in a Taylor series in remnant phase phi, which is small at very high correction, leading to a perturbed point-spread function (PSF) that is a sum of algebraic terms, each of distinct spatial symmetry. At sufficiently high correction, one need deal with only a few of the lowest-order terms. A first-order expansion gives an ideal PSF plus two terms, linear and quadratic, describing the two brightest, physically most relevant kinds of speckle. A second-order expansion gives three new terms, the brightest of which is primarily a static correction to the PSF, with a much smaller true speckle component. When the correction is great enough to isolate individual speckle terms, the two terms from the first-order expansion alone determine the essential physics. A general observational strategy is outlined for reducing speckle noise in highly corrected companion searches, dominated by a few speckle terms of definite spatial symmetry.

Anomalous intensity of pinned speckles at high adaptive correction.

Ground-based optical searches for faint stellar or planetary companions about other stars may be limited by speckle noise, which is the rapid intensity fluctuations that are due to motions of remnant atmospheric speckles. Adaptive optics (AO) can reduce residual wave-front phase errors to low values, substantially reducing the unwanted power in the speckle halo. At high correction, however, the noise in the halo will be dominated by anomalously bright "pinned" speckles that have a number of unusual properties. They can have negative intensities and will appear in spatially antisymmetric patterns; they are spatially pinned to Airy rings and have zero mean in a sufficiently long integration. Some of these properties may be used to reduce the unanticipated effect of pinned speckles on companion searches, depending on details of the AO system. But, in short exposures, pinned speckles dominate speckle noise over much of the inner halo for Strehl ratios S as low as 0.6 and over much of the outer halo too as Strehl and deformable-mirror actuator densities increase. I show that these anomalously bright pinned speckles are not included in the traditional expression for speckle power in an image, (1 - S), on which sensitivity estimates of future high-performance AO systems have been based.