Patrick J. Reardon

Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials

We use the two-dimensional Chebyshev polynomials as the basis for decomposition of test data over rectangular apertures, particularly for anamorphic optics. This includes simple optics such as cylindrical lenses and mirrors as well as complex optics, such as aspheric cylindrical optics. The new basis set is strictly orthogonal over rectangles of arbitrary aspect ratio and they correspond well with the aberrations of systems containing such type of optics. An example is given that applies the new basis set to study the surface figure error of a cylindrical Schmidt corrector plate. It is not only an excellent fitting basis but also can be used to flag misalignment errors that are critical to fabrication.

Schmidt-like corrector plate for cylindrical optics

We report initial results on designing and manufacturing a Schmidt-like corrector plate for a commercial off-the-shelf cylindrical lens, eliminating the cylindrical equivalent of its spherical aberration. The corrector is made by figuring the correction profile onto a precision glass window, which is subsequently aligned to the cylindrical lens. We have successfully fabricated the first plate and applied it in an interferometric test of a near-cylinder optic. The interferometric data from before and after applying the corrector demonstrates that the modified optic produces a cylindrical test wavefront with 25× reduction compared to the uncorrected case.

Results of the beryllium AMSD mirror cryogenic optical testing

The 1.4-meter semi-rigid, beryllium Advanced Mirror System Demonstrator (AMSD) mirror completed initial cryogenic testing at Marshall’s X-ray Calibration Facility (XRCF) in August of 2003. Results of this testing show the mirror to have very low cryogenic surface deformation and possess exceptional figure stability. Additionally, the mirror substrate exhibits virtually no change in surface figure over the James Webb Space Telescope (JWST) operational temperature range of 30 to 62 Kelvin. The lightweighted, semi-rigid mirror architecture approach demonstrated here is a precursor to the mirror technology being applied to the JWST observatory. Testing at ambient and cryogenic temperatures included the radius of curvature actuation system and the rigid body displacement system. These two systems incorporated the use of 4 actuators to allow the mirror to change piston, tilt, and radius of curvature. Presented here are the results of the figure change, alignment change, and radius change as a function of temperature. Also shown will be the actuator influence functions at both ambient and cryogenic temperatures.

Separating misalignment from misfigure in interferograms on cylindrical optics.

This paper presents an analytical method that allows for unambiguous separation of misalignment from the interferometric measurement of cylindrical optics with rectangular apertures. This method not only removes the misalignment-induced aberration from the measured wavefront data, but also yields the amount of misalignment in the test setup. We verified this method during testing of a convex cylindrical optic.

Determining parent radius and conic of an off-axis segment interferometrically with a spherical reference wave.

A simple interferometric method is presented for determining the parent radius of curvature (ROC) and conic constant (CC) of a conic surface. This method compares the test surface with a spherical reference wavefront having a ROC equal to the local sagittal, medial, or tangential ROC. The measured wavefront aberrations, particularly the astigmatism and coma, and local radii are used to determine the parent ROC and CC. This method does not require null optics or knowledge of the surface coordinate where the measurement is made.

Autonomous long-range open area fire detection and reporting

Approximately 5 billion dollars in US revenue was lost in 2003 due to open area fires. In addition many lives are lost annually. Early detection of open area fires is typically performed by manned observatories, random reporting and aerial surveillance. Optical IR flame detectors have been developed previously. They typically have experienced high false alarms and low flame detection sensitivity due to interference from solar and other causes. Recently a combination of IR detectors has been used in a two or three color mode to reduce false alarms from solar, or background sources. A combination of ultra-violet C (UVC) and near infra-red (NIR) detectors has also been developed recently for flame discrimination. Relatively solar-blind basic detectors are now available but typically detect at only a few tens of meters at ~ 1 square meter fuel flame. We quantify the range and solar issues for IR and visible detectors and qualitatively define UV sensor requirements in terms of the mode of operation, collection area issues and flame signal output by combustion photochemistry. We describe innovative flame signal collection optics for multiple wavelengths using UV and IR as low false alarm detection of open area fires at long range (8-10 km/m2) in daylight (or darkness). A circular array detector and UV-IR reflective and refractive devices including cylindrical or toroidal lens elements for the IR are described. The dispersion in a refractive cylindrical IR lens characterizes the fire and allows a stationary line or circle generator to locate the direction and different flame IR “colors” from a wide FOV. The line generator will produce spots along the line corresponding to the fire which can be discriminated with a linear detector. We demonstrate prototype autonomous sensors with RF digital reporting from various sites.

Multi-turn all-reflective optical gyroscope

We use calculation and simulation to characterize an all-reflective monolithic gyroscopic structure that supports 3 sets of orthogonal, spatially dense and continuous helical optical paths. This gyroscope differs from current fiber optic and ring laser gyroscopes primarily in the free space multi-turn nature of the optical path. The design also creates opportunities for introducing gain while minimizing spontaneous emission noise from those gain regions. The achievable angular measurement precision for each axis, given ideal components and no gain, is calculated to be ~0.001 degrees /hr for a structure of ~6.5 cm diameter, ~1 watt average optical power, and a wavelength of 0.5 microm. For fixed power, the uncertainty scales as the reciprocal cube of the diameter of the structure. While the fabrication and implementation requirements are challenging, the needed reflectivities and optical surface quality have been demonstrated in more conventional optics. In particular, the low mass, compact character, and all reflective optics offer advantages for applications in space.

First-order perturbations of reflective surfaces and their effects in interferometric testing of mirrors

The equations are derived which relate first-order perturbations of a mirror surface to the optical path difference (OPD) function observed during interferometric centre-of-curvature null tests. Rigid body displacements in particular and their effects on the Fourier coefficients of the OPD function are then considered. Next, the linearity of the rigid body component of the OPD is shown to lead to a method, based on the generalized matrix inverse, for aligning mirrors. Finally, the limits of the validity, in terms of the magnitude of local displacements, of our linear model are analysed. The result of the analysis is a concise, conceptually appealing treatment of general surface deformations in the interferometric regime and a matrix formulation for the particular case of rigid body displacements in the centre-of-curvature null interferometer configuration. This robust formulation treats interferometrically measured OPD functions as state vectors and small deformations as linear transformations of these vectors.

Regular geometries for folded optical modules

We present three new three-dimensional right-cylindrical folded modular interconnection architectures. To compare these systems among each other and with earlier designs, we introduce several figures of merit. The figures of merit describe such aspects of the system as the compactness, the relative angles of the optical axis to optical elements in the system, and system manufacturability. These figures of merit permit the designer of such an optical system to choose the geometry best suited for a particular application.

Distortion compensation in interferometric testing of mirrors

We present a method to compensate for the imaging distortion encountered in interferometric testing of mirrors, which is introduced by interferometer optics as well as from geometric projection errors. Our method involves placing a mask, imprinted with a regular square grid, over the mirror and finding a transformation that relates the grid coordinates to coordinates in the base plane of the parent surface. This method can be used on finished mirrors since no fiducials have to be applied to the surfaces. A critical step in the process requires that the grid coordinates be projected onto the mirror base plane before the regression is performed. We apply the method successfully during a center-of-curvature null test of an F/2 off-axis paraboloid.