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NASA NTRS2004

Constructing an Educational Mars Simulation

January 14th 2004, President George Bush announces his plans to catalyst the space program into a new era of space exploration and discovery. His vision encompasses a robotics program to explore our solar system, a return to the moon, the human exploration of Mars, and to promote international prosperity towards our endeavors. We at NASA now have the task of constructing this vision in a very real timeframe. I have been chosen to begin phase 1 of making this vision a reality. I will be working on creating an Educational Mars Simulation of human exploration of Mars to stimulate interest and involvement with the project from investors and the community. GRC s Computer Services Division (CSD) in collaboration with the Office of Education Programs will be designing models, constructing terrain, and programming this simulation to create a realistic portrayal of human exploration on mars. With recent and past technological breakthroughs in computing, my primary goal can be accomplished with only the aid of 3-4 software packages. Lightwave 3D is the modeling package we have selected to use for the creation of our digital objects. This includes a Mars pressurized rover, rover cockpit, landscape/terrain, and habitat. Once we have the models completed they need textured so Photoshop and Macromedia Fireworks are handy for bringing these objects to life. Before directly importing all of this data into a simulation environment, it is necessary to first render a stunning animation of the desired final product. This animation with represent what we hope to capture out of the simulation and it will include all of the accessories like ray-tracing, fog effects, shadows, anti-aliasing, particle effects, volumetric lighting, and lens flares. Adobe Premier will more than likely be used for video editing and adding ambient noises and music. Lastly, V-Tree is the real-time 3D graphics engine which will facilitate our realistic simulation. Additional information is included in the original extended abstract.

Henke, Stephen A.↗

NASA NTRS2006

Propagation Effects of Wind and Temperature on Acoustic Ground Contour Levels

Propagation characteristics for varying wind and temperature atmospheric conditions are identified using physically-limiting propagation angles to define shadow boundary regions. These angles are graphically illustrated for various wind and temperature cases using a newly developed ray-tracing propagation code.

Heath, Stephanie L.↗

NASA NTRS2006

Small-Scale Gravity Waves in ER-2 MMS/MTP Wind and Temperature Measurements during CRYSTAL-FACE

Lower stratospheric wind and temperature measurements made from NASA's high-altitude ER-2 research aircraft during the CRYSTAL-FACE campaign in July 2002 were analyzed to retrieve information on small scale gravity waves (GWs) at the aircraft's flight level (typically approximately 20 km altitude). For a given flight segment, the S-transform (a Gaussian wavelet transform) was used to search for and identify small horizontal scale GW events, and to estimate their apparent horizontal wavelengths. The horizontal propagation directions of the events were determined using the Stokes parameter method combined with the cross S-transform analysis. The vertical temperature gradient was used to determine the vertical wavelengths of the events. GW momentum fluxes were calculated from the cross S-transform. Other wave parameters such as intrinsic frequencies were calculated using the GW dispersion relation. More than 100GW events were identified. They were generally high frequency waves with vertical wavelength of approximately 5 km and horizontal wavelength generally shorter than 20 km. Their intrinsic propagation directions were predominantly toward the east, whereas their ground-based propagation directions were primarily toward the west. Among the events, approximately 20% of them had very short horizontal wavelength, very high intrinsic frequency, and relatively small momentum fluxes, and thus they were likely trapped in the lower stratosphere. Using the estimated GW parameters and the background winds and stabilities from the NCAR/NCEP reanalysis data, we were able to trace the sources of the events using a simple reverse ray-tracing. More than 70% of the events were traced back to convective sources in the troposphere, and the sources were generally located upstream of the locations of the events observed at the aircraft level. Finally, a probability density function of the reversible cooling rate due to GWs was obtained in this study, which may be useful for cirrus cloud models.

Wang, L.↗

NASA NTRS2008

How Very Massive Metal-Free Stars Start Cosmological Reionization

The initial conditions and relevant physics for the formation of the earliest galaxies are well specified in the concordance cosmology. Using ab initio cosmological Eulerian adaptive mesh refinement radiation hydrodynamical calculations, we discuss how very massive stars start the process of cosmological reionization. The models include nonequilibrium primordial gas chemistry and cooling processes and accurate radiation transport in the case B approximation using adaptively ray-traced photon packages, retaining the time derivative in the transport equation. Supernova feedback is modeled by thermal explosions triggered at parsec scales. All calculations resolve the local Jeans length by at least 16 grid cells at all times and as such cover a spatial dynamic range of approx.10(exp 6). These first sources of reionization are highly intermittent and anisotropic and first photoionize the small-scale voids surrounding the halos they form in, rather than the dense filaments they are embedded in. As the merging objects form larger, dwarf-sized galaxies, the escape fraction of UV radiation decreases and the H II regions only break out on some sides of the galaxies, making them even more anisotropic. In three cases, SN blast waves induce star formation in overdense regions that were formed earlier from ionization front instabilities. These stars form tens of parsecs away from the center of their parent DM halo. Approximately five ionizing photons are needed per sustained ionization when star formation in 10(exp 6) stellar Mass halos is dominant in the calculation. As the halos become larger than approx.10(exp 7) Stellar Mass, the ionizing photon escape fraction decreases, which in turn increases the number of photons per ionization to 15-50, in calculations with stellar feedback only. Radiative feedback decreases clumping factors by 25% when compared to simulations without star formation and increases the average temperature of ionized gas to values between 3000 and 10,000 K.

Wise, John H.↗

NASA NTRS2009

Fast Ray Tracing of Lunar Digital Elevation Models

Ray-tracing (RT) of Lunar Digital Elevation Models (DEM)'s is performed to virtually derive the degree of radiation incident to terrain as a function of time, orbital and ephemeris constraints [I- 4]. This process is an integral modeling process in lunar polar research and exploration due to the present paucity of terrain information at the poles and mission planning activities for the anticipated spring 2009 launch of the Lunar Reconnaissance Orbiter (LRO). As part of the Lunar Exploration Neutron Detector (LEND) and Lunar Crater Observation and Sensing Satellite (LCROSS) preparations RI methods are used to estimate the critical conditions presented by the combined effects of high latitude, terrain and the moons low obliquity [5-7]. These factors yield low incident solar illumination and subsequently extreme thermal, and radiation conditions. The presented research uses RT methods both for radiation transport modeling in space and regolith related research as well as to derive permanently shadowed regions (PSR)'s in high latitude topographic minima, e.g craters. These regions are of scientific and human exploration interest due to the near constant low temperatures in PSRs, inferred to be < 100 K. Hydrogen is thought to have accumulated in PSR's through the combined effects of periodic cometary bombardment and/or solar wind processes, and the extreme cold which minimizes hydrogen sublimation [8-9]. RT methods are also of use in surface position optimization for future illumination dependent on surface resources e.g. power and communications equipment.

McClanahan, Timothy P.↗

NASA NTRS2009

The Lunar Regolith as a Remote Sensing Target for the Lunar Reconnaissance Orbiter (LRO)

Of the 6 instruments and one technology demonstration aboard the LRO, only CRaTER does not measure some kind of interaction of particles with the lunar regolith. LEND detects neutron fluence that contains information about the number density of protons in the upper regolith. To infer the presence of protons, the PI must assume a model that characterizes the surface as a collection of atoms. Thus, LEND does not sense the regolith as a structure. LROC, LOLA, and LAMP sense reflected photons whose wavelength is much shorter than the median particle size in the regolith. The photons interact with electrons, either in atomic shells or in chemical bonds. These interactions occur within a nanometer or so of the surface of a particle. Thus, the particles are macroscopic objects and models of the reflection process invoke ray-tracing optics. DIVINER senses photons that have been emitted by surface particles through thermal phonon processes. The wavelengths detected by the instrument are of the same order as the median particle size, and the photons contain information on particle dimensions as well as the molecular bonds in the constituent compounds. The Mini-RF synthetic aperture radar generates and detects photons of a few centimeters wavelength that interact with the regolith as a dielectric, the dielectric properties of the particulate component being described through effective medium theory. However, the interaction with rocks (macroscopic objects of interest to geologists) can be characterized using Fresnel or Mie models of electromagnetic properties.

Mendell, Wendell W.↗

NASA NTRS2008

Effect of the Inhomogeneity of Ice Crystals on Retrieving Ice Cloud Optical Thickness and Effective Particle Size

Spherical or spheroidal air bubbles are generally trapped in the formation of rapidly growing ice crystals. In this study the single-scattering properties of inhomogeneous ice crystals containing air bubbles are investigated. Specifically, a computational model based on an improved geometric-optics method (IGOM) has been developed to simulate the scattering of light by randomly oriented hexagonal ice crystals containing spherical or spheroidal air bubbles. A combination of the ray-tracing technique and the Monte Carlo method is used. The effect of the air bubbles within ice crystals is to smooth the phase functions, diminish the 22deg and 46deg halo peaks, and substantially reduce the backscatter relative to bubble-free particles. These features vary with the number, sizes, locations and shapes of the air bubbles within ice crystals. Moreover, the asymmetry factors of inhomogeneous ice crystals decrease as the volume of air bubbles increases. Cloud reflectance lookup tables were generated at wavelengths 0.65 m and 2.13 m with different air-bubble conditions to examine the impact of the bubbles on retrieving ice cloud optical thickness and effective particle size. The reflectances simulated for inhomogeneous ice crystals are slightly larger than those computed for homogenous ice crystals at a wavelength of 0.65 microns. Thus, the retrieved cloud optical thicknesses are reduced by employing inhomogeneous ice cloud models. At a wavelength of 2.13 microns, including air bubbles in ice cloud models may also increase the reflectance. This effect implies that the retrieved effective particle sizes for inhomogeneous ice crystals are larger than those retrieved for homogeneous ice crystals, particularly, in the case of large air bubbles.

Xie, Yu↗

NASA NTRS2007

Rapid Analysis of Mass Distribution of Radiation Shielding

Radiation Shielding Evaluation Toolset (RADSET) is a computer program that rapidly calculates the spatial distribution of mass of an arbitrary structure for use in ray-tracing analysis of the radiation-shielding properties of the structure. RADSET was written to be used in conjunction with unmodified commercial computer-aided design (CAD) software that provides access to data on the structure and generates selected three-dimensional-appearing views of the structure. RADSET obtains raw geometric, material, and mass data on the structure from the CAD software. From these data, RADSET calculates the distribution(s) of the masses of specific materials about any user-specified point(s). The results of these mass-distribution calculations are imported back into the CAD computing environment, wherein the radiation-shielding calculations are performed.

Zapp, Edward↗

NASA NTRS2010

Effect of Anatomical Modeling on Space Radiation Dose Estimates: A Comparison of Doses for NASA Phantoms and 5th, 50th, and 95th Percentile UF Hybrid Phantoms

The estimate of absorbed dose to individual organs of a space crewmember is affected by the geometry of the anatomical model of the astronaut used in the radiation transport calculation. For astronaut dosimetry, NASA currently uses the computerized anatomical male (CAM) and computerized anatomical female (CAF) stylized phantoms to represent astronauts in its operational radiation dose analyses. These phantoms are available in one size and in two body positions. In contrast, the UF Hybrid Adult Male and Female (UFHADM and UFHADF) phantoms have organ shapes based on actual CT data. The surfaces of these phantoms are defined by non-uniform rational B-spline surfaces, and are thus flexible in terms of body morphometry and extremity positioning. In this study, UFHADM and UFHADF are scaled to dimensions corresponding to 5th, 50th, and 95th percentile (PCTL) male and female astronauts. A ray-tracing program is written in Visual Basic 2008, which is then used to create areal density maps for dose points corresponding to various organs within the phantoms. The areal density maps, along with appropriate space radiation spectra, are input into the NASA program couplet HZETRN/BRYNTRN, and organ doses are calculated. The areal density maps selected tissues and organs of the 5th, 50th, and 95th PCTL male and female phantoms are presented and compared. In addition, the organ doses for the 5th, 50th, and 95th PCTL male and female phantoms are presented and compared to organ doses for CAM and CAF.

Bahadori, A.↗

NASA NTRS2004

Gravity Waves and Mesospheric Clouds in the Summer Middle Atmosphere: A Comparison of Lidar Measurements and Ray Modeling of Gravity Waves Over Sondrestrom, Greenland

We conducted gravity wave ray-tracing experiments within an atmospheric region centered near the ARCLITE lidar system at Sondrestrom, Greenland (67N, 310 deg E), in efforts to understand lidar observations of both upper stratospheric gravity wave activity and mesospheric clouds during August 1996 and the summer of 2001. The ray model was used to trace gravity waves through realistic three-dimensional daily-varying background atmospheres in the region, based on forecasts and analyses in the troposphere and stratosphere and climatologies higher up. Reverse ray tracing based on upper stratospheric lidar observations at Sondrestrom was also used to try to objectively identify wave source regions in the troposphere. A source spectrum specified by reverse ray tracing experiments in early August 1996 (when atmospheric flow patterns produced enhanced transmission of waves into the upper stratosphere) yielded model results throughout the remainder of August 1996 that agreed best with the lidar observations. The model also simulated increased vertical group propagation of waves between 40 km and 80 km due to intensifying mean easterlies, which allowed many of the gravity waves observed at 40 km over Sondrestrom to propagate quasi-vertically from 40-80 km and then interact with any mesospheric clouds at 80 km near Sondrestrom, supporting earlier experimentally-inferred correlations between upper stratospheric gravity wave activity and mesospheric cloud backscatter from Sondrestrom lidar observations. A pilot experiment of real-time runs with the model in 2001 using weather forecast data as a low-level background produced less agreement with lidar observations. We believe this is due to limitations in our specified tropospheric source spectrum, the use of climatological winds and temperatures in the upper stratosphere and mesosphere, and missing lidar data from important time periods.

LIDAR (LIGHT DETECTION AND RANGING)↗

NASA NTRS2003

Predicting and Managing Lighting and Visibility for Human Operations in Space

Lighting is critical to human visual performance. On earth this problem is well understood and solutions are well defined and executed. Because the sun rises and sets on average every 45 minutes during Earth orbit, humans working in space must cope with ~ extremely dynamic lighting conditions varying from very low light conditions to severe glare and contrast conditions. For critical operations, it is essential that lighting conditions be predictable and manageable. Mission planners need to detelmine whether low-light video cameras are required or whether additional luminaires, or lamps, need to be flown . Crew and flight directors need to have up to date daylight orbit time lines showing the best and worst viewing conditions for sunlight and shadowing. Where applicable and possible, lighting conditions need to be part of crew training. In addition, it is desirable to optimize the quantity and quality of light because of the potential impacts on crew safety, delivery costs, electrical power and equipment maintainability for both exterior and interior conditions. Addressing these issues, an illumination modeling system has been developed in the Space Human Factors Laboratory at ASA Johnson Space Center. The system is the integration of a physically based ray-tracing package ("Radiance"), developed at the Lawrence Berkeley Laboratories, a human factors oriented geometric modeling system developed by NASA and an extensive database of humans and their work environments. Measured and published data has been collected for exterior and interior surface reflectivity; luminaire beam spread distribution, color and intensity and video camera light sensitivity and has been associated with their corresponding geometric models. Selecting an eye-point and one or more light sources, including sun and earthshine, a ~ snapshot of the light energy reaching the surfaces or reaching the eye point is computed. This energy map is then used to extract the required information needed for useful predictions. Using a validated, comprehensive illumination model integrated with empirically derived data, predictions of lighting and viewing conditions have been successfully used for Shuttle and Space Station planning and assembly operations. It has successfully balanced the needs for adequate human performance with the utili zation of resources. Keywords: Modeling, ray tracing, luminaires, refl ectivity, luminance, illuminance.

Maida, James C.↗

NASA NTRS2011

A Deterministic Electron, Photon, Proton and Heavy Ion Radiation Transport Suite for the Study of the Jovian System

A deterministic suite of radiation transport codes, developed at NASA Langley Research Center (LaRC), which describe the transport of electrons, photons, protons, and heavy ions in condensed media is used to simulate exposures from spectral distributions typical of electrons, protons and carbon-oxygen-sulfur (C-O-S) trapped heavy ions in the Jovian radiation environment. The particle transport suite consists of a coupled electron and photon deterministic transport algorithm (CEPTRN) and a coupled light particle and heavy ion deterministic transport algorithm (HZETRN). The primary purpose for the development of the transport suite is to provide a means for the spacecraft design community to rapidly perform numerous repetitive calculations essential for electron, proton and heavy ion radiation exposure assessments in complex space structures. In this paper, the radiation environment of the Galilean satellite Europa is used as a representative boundary condition to show the capabilities of the transport suite. While the transport suite can directly access the output electron spectra of the Jovian environment as generated by the Jet Propulsion Laboratory (JPL) Galileo Interim Radiation Electron (GIRE) model of 2003; for the sake of relevance to the upcoming Europa Jupiter System Mission (EJSM), the 105 days at Europa mission fluence energy spectra provided by JPL is used to produce the corresponding dose-depth curve in silicon behind an aluminum shield of 100 mils ( 0.7 g/sq cm). The transport suite can also accept ray-traced thickness files from a computer-aided design (CAD) package and calculate the total ionizing dose (TID) at a specific target point. In that regard, using a low-fidelity CAD model of the Galileo probe, the transport suite was verified by comparing with Monte Carlo (MC) simulations for orbits JOI--J35 of the Galileo extended mission (1996-2001). For the upcoming EJSM mission with a potential launch date of 2020, the transport suite is used to compute the traditional aluminum-silicon dose-depth calculation as a standard shield-target combination output, as well as the shielding response of high charge (Z) shields such as tantalum (Ta). Finally, a shield optimization algorithm is used to guide the instrument designer with the choice of graded-Z shield analysis.

Norman, Ryan B.↗

NASA NTRS2010

Prospects for UT1 Measurements from VLBI Intensive Sessions

Very Long Baseline Interferometry (VLBI) Intensives are one-hour single baseline sessions to provide Universal Time (UT1) in near real-time up to a delay of three days if a site is not e-transferring the observational data. Due to the importance of UT1 estimates for the prediction of Earth orientation parameters, as well as any kind of navigation on Earth or in space, there is not only the need to improve the timeliness of the results but also their accuracy. We identify the asymmetry of the tropospheric delays as the major error source, and we provide two strategies to improve the results, in particular of those Intensives which include the station Tsukuba in Japan with its large tropospheric variation. We find an improvement when (1) using ray-traced delays from a numerical weather model, and (2) when estimating tropospheric gradients within the analysis of Intensive sessions. The improvement is shown in terms of reduction of rms of length-of-day estimates w.r.t. those derived from Global Positioning System observations

Boehm, Johannes↗

NASA NTRS2011

General Tool for Evaluating High-Contrast Coronagraphic Telescope Performance Error Budgets

The Coronagraph Performance Error Budget (CPEB) tool automates many of the key steps required to evaluate the scattered starlight contrast in the dark hole of a space-based coronagraph. The tool uses a Code V prescription of the optical train, and uses MATLAB programs to call ray-trace code that generates linear beam-walk and aberration sensitivity matrices for motions of the optical elements and line-of-sight pointing, with and without controlled fine-steering mirrors (FSMs). The sensitivity matrices are imported by macros into Excel 2007, where the error budget is evaluated. The user specifies the particular optics of interest, and chooses the quality of each optic from a predefined set of PSDs. The spreadsheet creates a nominal set of thermal and jitter motions, and combines that with the sensitivity matrices to generate an error budget for the system. CPEB also contains a combination of form and ActiveX controls with Visual Basic for Applications code to allow for user interaction in which the user can perform trade studies such as changing engineering requirements, and identifying and isolating stringent requirements. It contains summary tables and graphics that can be instantly used for reporting results in view graphs. The entire process to obtain a coronagraphic telescope performance error budget has been automated into three stages: conversion of optical prescription from Zemax or Code V to MACOS (in-house optical modeling and analysis tool), a linear models process, and an error budget tool process. The first process was improved by developing a MATLAB package based on the Class Constructor Method with a number of user-defined functions that allow the user to modify the MACOS optical prescription. The second process was modified by creating a MATLAB package that contains user-defined functions that automate the process. The user interfaces with the process by utilizing an initialization file where the user defines the parameters of the linear model computations. Other than this, the process is fully automated. The third process was developed based on the Terrestrial Planet Finder coronagraph Error Budget Tool, but was fully automated by using VBA code, form, and ActiveX controls.

Marchen, Luis F.↗

NASA NTRS2005

Measuring Low-Order Aberrations in a Segmented Telescope

The in-focus PSF optimizer (IPO) is an algorithm for use in monitoring and controlling the alignment of the segments of a segmented-mirror astronomical telescope. IPO is so named because it computes wave-front aberrations of the telescope from digitized pointspread functions (PSFs) measured in infocus images. Inasmuch as distant astronomical objects that behave optically as point sources can typically be seen in almost any astronomical image, the main benefit afforded by IPO may be to enable maintenance of mirror-segment alignments without detracting from valuable scientific-observation time. IPO evolved from prescription-retrieval type algorithms. Prescription retrieval uses in-focus and out-of-focus PSFs to infer the state of an imaging optical system. The state, in this context, refers to the positions, orientations, and low-order figure errors of the optical elements in the system. Both prescription- retrieval and IPO use an iterative, nonlinear, least-squares optimizer to compute the optimal state parameters such that a digital computer-generated model image matches the digitized image acquired from the real system. The difference between IPO and prescription- retrieval algorithms is that IPO is specifically designed to utilize infocus images only. Although the restriction to in-focus images limits IPO to calculating only the lowest-order wave front aberrations, it also causes the resulting computation to take much less time because fewer degrees of freedom are included in the optimization process. In the prescription retrieval software developed at JPL, the model images are generated using the ray-trace/physical optics program, MACOS. IPO, on the other hand, uses a linear sensitivity matrix to compute the exit-pupil wave front from the system parameters; the wave front is then converted into a complex pupil field, which is then propagated to the image plane via a fast Fourier transform. This approach is computationally faster and requires less computer memory than is needed for prescription retrieval.

Ohara, Catherine↗

NASA NTRS2012

Thermal Stability of Frozen Volatiles in the North Polar Region of Mercury

Earth-based radar observations have revealed the presence on Mercury of anomalously bright, depolarizing features that appear to be localized in the permanently shadowed regions of high-latitude impact craters [1]. Observations of similar radar signatures over a range of radar wavelengths implies that they correspond to deposits that are highly transparent at radar wavelengths and extend to depths of several meters below the surface [1]. Thermal models using idealized crater topographic profiles have predicted the thermal stability of surface and subsurface water ice at these same latitudes [2]. One of the major goals of the MESSENGER mission is to characterize the nature of radar-bright craters and presumed associated frozen volatile deposits at the poles of Mercury through complementary orbital observations by a suite of instruments [3]. Here we report on an examination of the thermal stability of water ice and other frozen volatiles in the north polar region of Mercury using topographic profiles obtained by the Mercury Laser Altimeter (MLA) instrument [4] in conjunction with a three-dimensional ray-tracing thermal model previously used to study the thermal environment of polar craters on the Moon [5].

Paige, David A.↗

NASA NTRS2012

A Framework for Simulation of Aircraft Flyover Noise Through a Non-Standard Atmosphere

This paper describes a new framework for the simulation of aircraft flyover noise through a non-standard atmosphere. Central to the framework is a ray-tracing algorithm which defines multiple curved propagation paths, if the atmosphere allows, between the moving source and listener. Because each path has a different emission angle, synthesis of the sound at the source must be performed independently for each path. The time delay, spreading loss and absorption (ground and atmosphere) are integrated along each path, and applied to each synthesized aircraft noise source to simulate a flyover. A final step assigns each resulting signal to its corresponding receiver angle for the simulation of a flyover in a virtual reality environment. Spectrograms of the results from a straight path and a curved path modeling assumption are shown. When the aircraft is at close range, the straight path results are valid. Differences appear especially when the source is relatively far away at shallow elevation angles. These differences, however, are not significant in common sound metrics. While the framework used in this work performs off-line processing, it is conducive to real-time implementation.

Arntzen, Michael↗

NASA NTRS2012

Telescope Alignment From Sparsely Sampled Wavefront Measurements Over Pupil Subapertures

Alignment of two-element telescopes is a classic problem. During recent integration and test of the Space Interferometry Mission s (SIM s) Astrometric Beam Combiner (ABC), the innovators were faced with aligning two such telescope subsystems in the presence of a further complication: only two small subapertures in each telescope s pupil were accessible for measuring the wavefront with a Fizeau interferometer. This meant that the familiar aberrations that might be interpreted to infer system misalignments could be viewed only over small sub-regions of the pupil, making them hard to recognize. Further, there was no contiguous surface of the pupil connecting these two subapertures, so relative phase piston information was lost; the underlying full-aperture aberrations therefore had an additional degree of ambiguity. The solution presented here is to recognize that, in the absence of phase piston, the Zygo measurements primarily provide phase tilt in the subaperture windows of interest. Because these windows are small and situated far from the center of the (inaccessible) unobscured full aperture, any aberrations that are higher-order than tilt will be extremely high-order on the full aperture, and so not necessary or helpful to the alignment. Knowledge of the telescope s optical prescription allows straightforward evaluation of sensitivities (subap mode strength per unit full-aperture aberration), and these can be used in a predictive matrix approach to move with assurance to an aligned state. The technique is novel in every operational way compared to the standard approach of alignment based on full-aperture aberrations or searching for best rms wavefront. This approach is closely grounded in the observable quantities most appropriate to the problem. It is also more intuitive than inverting full phase maps (or subaperture Zernike spectra) with a ray-tracing program, which must certainly work in principle, but in practice met with limited success. Even if such classical alignment techniques became practical, the techniques reported here form a reassuringly transparent and intuitive check on the course of the alignment with very little computational effort.

Bloemhof, Eric E.↗