Brian M. Robinson

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.

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.

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.

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.

Advanced technology solar telescope multiple Fabry-Pérot interferometer telecentric optical design

We present four preliminary designs for a telecentric optical train supporting the Advanced Technology Solar Telescope (ATST) multiple Fabry-Perot interferometer (MFPI), which is to be used as an imaging spectrometer and imaging spectropolarimeter. The point of departure for all three designs is the F/40 telecentric image at the Coude focus of the ATST. The first design, representing the high-spectral-resolution mode of operation, produces an intermediate F/300 telecentric image within the triple etalon system and a 34-arcsec field of view (FOV). The second design, intermediate between high- and low-spectral-resolution modes of operation, produces an intermediate F/150 telecentric image at the etalons and a 1.1-arcmin FOV. The third and fourth designs each represent a low-resolution mode of operation, producing an F/82 telecentric image at the etalons and a 2-arcmin FOV. Each design results in good telecentricity and image quality. Departures from telecentricity at the intermediate image plane cause field-dependent shifts of the bandpass peak, which are negligible compared to the bandpass FWHM. The root mean square (rms) geometric spot sizes at the final image plane fit well within the area of a camera pixel, which is itself in accordance with the Nyquist criterion, half the width of the 28-µm-wide resolution element (as determined from the diffraction limit of the ATST). For each configuration, we also examine the impact that the Beckers effect (the pupil apodization caused by the angle-dependent amplitude transmittance of the MFPI) has on the image quality of the MFPI instrument.

Advanced mirror system demonstrator cryogenic test error budget

The successful augmentation of NASAs X-Ray Cryogenic Facility (XRCF) at the Marshall Space Flight Center (MSFC) to an optical metrology testing facility for the Sub-scale Beryllium Mirror Demonstrator (SBMD) and NGST Mirror Sub-scale Demonstrator (NMSD) programs required significant modifications and enhancements to achieve reliable data. In addition to building and integrating both a helium shroud and a rugged, stable platform to support a wavefront sensor, a custom sensor suite was assembled and integrated to meet the test requirements. The metrology suite consisted of a high-resolution Shack-Hartmann sensor, a point diffraction interferometer, a point spread function camera, and a radius of curvature measuring device. The evolution from the SBMD and NMSD tests to the Advanced Mirror System Demonstrator (AMSD) program is less dramatic in some ways, such as the reutilization of the existing helium shroud and sensor support structure. However, significant modifications were required to meet the AMSD programs more stringent test requirements and conditions resulting in a substantial overhaul of the sensor suite and test plan. This paper will discuss the instrumentation changes made for AMSD, including the interferometer selection and null optics. The error budget for the tests will be presented using modeling and experimental data. We will show how the facility is ready to meet the test requirements.

Evolution strategies optimization of the multiple Fabry-Perót imaging interferometer for the advanced technology solar telescope

We describe an evolutionary algorithm for the design of an imaging triple-etalon Fabry-Perot interferometer (MFPI), which gives a solution to the multidimensional minimization process through a stochastic search method. The interactions between design variables (the etalon reflectances, interetalon ghost attenuator transmittances, and spacing ratios) are complex, resulting in a fitness landscape that is pitted with local optima. Traditional least-squares and gradient descent algorithms are not useful in such a situation. Instead, we employ a method called evolution strategies in which several preliminary designs are randomly generated subject to constraints. These designs are combined in pairs to produce offspring designs. The offspring population is mutated randomly, and only the fittest designs of the combined population are passed to the next iteration of the evolutionary process. We discuss the evolution strategies method itself, as well as its application to the specific problem of the design of an incoherently coupled triple-etalon interferometer intended for use as a focal plane instrument in the planned National Solar Observatorys Advanced Technology Solar Telescope (NSOs ATST). The algorithm converges quickly to a reasonable design that is well within the constraints imposed on the design variables, and which fulfills all resolution, signal-to-noise, throughput, and parasitic band suppression requirements.

Large Field-of-view KD*P Modulator for Solar Polarization Measurements

This paper will describe the evolution of the Marshall Space Flight Centers (MSFC) electro-optical polarimeter with emphasis on the field-of-view characteristics of the KD*P modulator. Understanding those characteristics was essential to the success of the MSFC solar vector magnetograph. The paper will show how the field-of-view errors of KD*P look similar to the linear polarization patterns seen in simple sunspots and why the placement of the KD*P in a collimated beam was essential in separating the instrumental polarization from the solar signal. Finally, this paper will describe a modulator design which minimizes those field-of-view errors.

Modeling and simulation of a spectro-polarimetric lenslet array imager

Abstract. A new, economical, lenslet-array-based imaging sensor design is proposed, simulated, and analyzed. In this investigation a bare lenslet array model is first developed in Code V®. The results show that, as expected, intolerable optical cross-talk is present in this simple system. This problem has been addressed in previous systems via the inclusion of a physical image separation layer. The alternative system proposed here to alleviate crosstalk involves the introduction of both polarizers and spectral filters. As a consequence this simple system design also provides spectro-polarimetric resolution. Simulations were developed in order to analyze the system performance of two designs. The simulation results were analyzed in terms of a measure of signal-to-noise ratio (SNR) and in terms of an en-squared energy that includes all subimages. The results show that a design employing only a few spectral filters suppresses crosstalk for objects of small angular extent but does not suppress crosstalk to a tolerable level for 2π steradian illumination, as evidenced by SNR less than one. However, the inclusion of more spectral filters results in a spectro-polarimetric thin imager design that suppresses crosstalk and provides finer spectral resolution without the inclusion of a signal separation layer.

Mirror Prescription Regression: A Differential Interferometric Technique

We present a remote, differential method for measuring the prescription of aspheric mirrors using null interferometry in the center-of-curvature configuration. The method requires no equipment beyond that used in a basic interferometery setup (i.e., there are no shearing elements or absolute distance meters). We chose this configuration because of its widespread use. However, the method is generalizable to other configurations with an adjustment of the governing equation. The method involves taking a series of interferograms before and after small, known misalignments are applied to the mirror in the interferometry setup and calculating the prescription (e.g., radius of curvature and conic constant) of the mirror, based on these differential measurements, using a nonlinear regression. We apply this method successfully to the testing of a Space Optics Research Lab off-axis parabola with a known focal length of 152.4 mm, a diameter of 76.2 mm, and an off-axis angle of 12°.