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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

High-Flux, High-Temperature Thermal Vacuum Qualification Testing of a Solar Receiver Aperture Shield

As part of the International Space Station (ISS) Phase 1 program, NASA Lewis Research Center (LERC) and the Russian Space Agency (RSA) teamed together to design, build and flight test the world's first orbital Solar Dynamic Power System (SDPS) on the Russian space station Mir. The Solar Dynamic Flight Demonstration (SDFD) program was to operate a nominal 2 kWe SDPS on Mir for a period up to 1-year starting in late 1997. Unfortunately, the SDFD mission was demanifested from the ISS phase 1 shuttle program in early 1996. However, substantial flight hardware and prototypical flight hardware was built including a heat receiver and aperture shield. The aperture shield comprises the front face of the cylindrical cavity heat receiver and is located at the focal plane of the solar concentrator. It is constructed of a stainless steel plate with a 1-m outside diameter, a 0.24-m inside diameter and covered with high-temperature, refractory metal Multi-Foil Insulation (MFI). The aperture shield must minimize heat loss from the receiver cavity, provide a stiff, high strength structure to accommodate shuttle launch loads and protect receiver structures from highly concentrated solar fluxes during concentrator off-pointing events. To satisfy Mir operational safety protocols, the aperture shield was required to accommodate direct impingement of the intensely concentrated solar image for a 1-hour period. To verify thermal-structural durability under the anticipated high-flux, high-temperature loading, an aperture shield test article was constructed and underwent a series of two tests in a large thermal vacuum chamber configured with a reflective, point-focus solar concentrator and a solar simulator. The test article was positioned near the focal plane and exposed to concentrated solar flux for a period of 1-hour. In the first test, a near equilibrium temperature of 1862 K was attained in the center of the shield hot spot. In the second test, with increased incident flux, a near equilibrium temperature of 2072 K was achieved. The aperture shield sustained no visible damage as a result of the exposures. This paper describes the aperture shield thermal-vacuum qualification test program including the test article, test facility, procedures, data collection, test success criteria, results and conclusions.

Kerslake, Thomas W.↗
NASA NTRS2004

The scaling relationship between telescope cost and aperture size for very large telescopes

Cost data for ground-based telescopes of the last century are analyzed for trends in the relationship between aperture size and cost. We find that for apertures built prior to 1980, costs scaled as aperture size to the 2.8 power, which is consistent with the precious finding of Meinel (1978). After 1980, 'traditional' monolithic mirror telescope costs have scaled as aperture to the 2.5 power. The large multiple mirror telescopes built or in construction during this time period (Keck, LBT, GTC) appear to deviate from this relationship with significant cost savings as a result, although it is unclear what power law such structures follow. We discuss the implications of the current cost-aperture size data on the proposed large telescope projects of the next ten to twenty years. Structures that naturally tend towards the 2.0 power in the cost-aperture relationship will be the favorable choice for future extremely large apertures; out expectation is that space-based structures will ultimately gain economic advantage over ground-based ones.

telescope costs↗
NASA NTRS2010

Two-Dimensional Synthetic-Aperture Radiometer

A two-dimensional synthetic-aperture radiometer, now undergoing development, serves as a test bed for demonstrating the potential of aperture synthesis for remote sensing of the Earth, particularly for measuring spatial distributions of soil moisture and ocean-surface salinity. The goal is to use the technology for remote sensing aboard a spacecraft in orbit, but the basic principles of design and operation are applicable to remote sensing from aboard an aircraft, and the prototype of the system under development is designed for operation aboard an aircraft. In aperture synthesis, one utilizes several small antennas in combination with a signal processing in order to obtain resolution that otherwise would require the use of an antenna with a larger aperture (and, hence, potentially more difficult to deploy in space). The principle upon which this system is based is similar to that of Earth-rotation aperture synthesis employed in radio astronomy. In this technology the coherent products (correlations) of signals from pairs of antennas are obtained at different antenna-pair spacings (baselines). The correlation for each baseline yields a sample point in a Fourier transform of the brightness-temperature map of the scene. An image of the scene itself is then reconstructed by inverting the sampled transform. The predecessor of the present two-dimensional synthetic-aperture radiometer is a one-dimensional one, named the Electrically Scanned Thinned Array Radiometer (ESTAR). Operating in the L band, the ESTAR employs aperture synthesis in the cross-track dimension only, while using a conventional antenna for resolution in the along-track dimension. The two-dimensional instrument also operates in the L band to be precise, at a frequency of 1.413 GHz in the frequency band restricted for passive use (no transmission) only. The L band was chosen because (1) the L band represents the long-wavelength end of the remote- sensing spectrum, where the problem of achieving adequate spatial resolution is most critical and (2) imaging airborne instruments that operate in this wavelength range and have adequate spatial resolution are difficult to build and will be needed in future experiments to validate approaches for remote sensing of soil moisture and ocean salinity. The two-dimensional instrument includes a rectangular array of patch antennas arranged in the form of a cross. The ESTAR uses analog correlation for one dimension, whereas the two-dimensional instrument uses digital correlation. In two dimensions, many more correlation pairs are needed and low-power digital correlators suitable for application in spaceborne remote sensing will help enable this technology. The two-dimensional instrument is dual-polarized and, with modification, capable of operating in a polarimetric mode. A flight test of the instrument took place in June 2003 and it participated in soil moisture experiments during the summers of 2003 and 2004.

LeVine, David M.↗
NASA NTRS2010

Self-Referencing Hartmann Test for Large-Aperture Telescopes

A method is proposed for end-to-end, full aperture testing of large-aperture telescopes using an innovative variation of a Hartmann mask. This technique is practical for telescopes with primary mirrors tens of meters in diameter and of any design. Furthermore, it is applicable to the entire optical band (near IR, visible, ultraviolet), relatively insensitive to environmental perturbations, and is suitable for ambient laboratory as well as thermal-vacuum environments. The only restriction is that the telescope optical axis must be parallel to the local gravity vector during testing. The standard Hartmann test utilizes an array of pencil beams that are cut out of a well-corrected wavefront using a mask. The pencil beam array is expanded to fill the full aperture of the telescope. The detector plane of the telescope is translated back and forth along the optical axis in the vicinity of the nominal focal plane, and the centroid of each pencil beam image is recorded. Standard analytical techniques are then used to reconstruct the telescope wavefront from the centroid data. The expansion of the array of pencil beams is usually accomplished by double passing the beams through the telescope under test. However, this requires a well-corrected, autocollimation flat, the diameter or which is approximately equal to that of the telescope aperture. Thus, the standard Hartmann method does not scale well because of the difficulty and expense of building and mounting a well-corrected, large aperture flat. The innovation in the testing method proposed here is to replace the large aperture, well-corrected, monolithic autocollimation flat with an array of small-aperture mirrors. In addition to eliminating the need for a large optic, the surface figure requirement for the small mirrors is relaxed compared to that required of the large autocollimation flat. The key point that allows this method to work is that the small mirrors need to operate as a monolithic flat only with regard to tip/tilt and not piston because in collimated space piston has no effect on the image centroids. The problem of aligning the small mirrors in tip/tilt requires a two-part solution. First, each mirror is suspended from a two-axis gimbal. The orientation of the gimbal is maintained by gravity. Second, the mirror is aligned such that the mirror normal is parallel to gravity vector. This is accomplished interferometrically in a test fixture. Of course, the test fixture itself needs to be calibrated with respect to gravity.

Korechoff, Robert P.↗
DOE OSTI2023

Comparative Analysis of Imaging and Measurements of Micrometer-Scale Fracture Aperture Fields Within a Heterogeneous Rock Using PET and X-ray CT

Knowledge of the spatial distribution of fracture apertures is essential for reliable characterization of flow and transport processes in fractured systems and for better understanding of physicochemical matrix–fracture interactions. Here, we propose and test two image-based methods, thereby extending the current experimental capabilities to characterize aperture size distribution in structurally heterogeneous geologic porous media noninvasively. The first approach utilizes an inversion method based on the dataset acquired from positron emission tomography (PET) and the second approach considers an extension of the classic missing attenuation technique that relies on clinical X-ray computed tomography (X-ray CT). Independent sets of imaging experiments are conducted on a fractured basalt core with heterogeneous matrix properties and aperture distributions to compare the two methodologies. A repeat of each experiment is conducted to verify the proposed workflows. The performance of these two imaging techniques is systematically evaluated through the analysis of signal-to-noise ratio, minimum fracture size detectability, and measurement errors. While both approaches provide a reliable estimation of fracture aperture distributions, PET yields a signal-to-noise ratio that is substantially higher than the corresponding X-ray CT measurements. Furthermore, uncertainties of the aperture values for PET are considerably lower ($\bar {\sigma}_{\text {d}} = 15\%$) compared to those obtained from X-ray CT ($\bar {\sigma}_{\text {d}} = 29\%$), allowing for the detection of minimum aperture sizes of 20 $\mu$m with 70% confidence level. Finally, these approaches provide key experimental tools for better understanding dynamic hydromechanical fracture properties in geologic systems.

58 GEOSCIENCES↗
DOE OSTI2020

A novel sector mass spectrograph design for high-order coded aperture Mass Spectrometry with stigmatic aberration correction

Previous works experimentally demonstrated that the application of spatially-coded apertures to simple sector mass spectrographs can result in increased signal intensity while maintaining spectral resolution comparable to that of a conventional slit aperture.[Chen, E.X., et al.: J Am Soc Mass Spectr. 26, 1633 (2015)][Russell, Z.E., et al.: J Am Soc Mass Spectr. 26, 248 (2015)] This spatial coding technique was later applied to a double-focusing Mattauch-Herzog mass spectrograph, and shown to be generally compatible with the architecture.[Russell, Z.E., et al.: J Am Soc Mass Spectr. 27, 1 (2016)] However, the achieved signal gain was limited by the spatial size of the electric sector gap. In this work, we introduce a modified version of the Mattauch-Herzog mass spectrograph with a wide-gap electric sector that is enabled by a novel, segmented-electrode approach, and show via simulation that this modified architecture alone (without aperture coding) achieves a 1.8x improvement in mass resolving power compared to a conventional Mattauch-Herzog spectrograph of equivalent size. Further, simulation of an aperture-coded version of the instrument supports a predicted signal strength increase of 50x with minimal loss of aperture clarity on the sensor due to the increased open area of the high-order coded aperture which can be passed.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

A coded aperture with sub-mean-free-path thickness for implosion geometry imaging on ICF and IFE experiments

Inertial confinement fusion and inertial fusion energy experiments diagnose the geometry of the fusion region through imaging of the neutrons released through fusion reactions. Pinhole arrays typically used for such imaging require thick substrates to obtain high contrast along with a small pinhole diameter to obtain high resolution capability, resulting in pinholes that have large aspect ratios. This leads to expensive pinhole arrays that have small solid angles and are difficult to align. Here, we propose a coded aperture with scatter and partial attenuation (CASPA) for fusion neutron imaging that relaxes the thick substrate requirement for good image contrast. These coded apertures are expected to scale to larger solid angles and are easier to align without sacrificing imaging resolution or throughput. We use Monte Carlo simulations (Geant4) to explore a coded aperture design to measure neutron implosion asymmetries on fusion experiments at the National Ignition Facility (NIF) and discuss the viability of this technique, matching the current nominal resolution of 10 µm. The results show that a 10 mm thick tungsten CASPA can image NIF implosions with neutron yields above 10 14 with quality comparable to unprocessed data from a current NIF neutron imaging aperture. Furthermore, this CASPA substrate is 20 times thinner than the current aperture arrays for fusion neutron imaging and less than one mean free-path of 14.1 MeV neutrons through the substrate. Since the resolution, solid angle, and throughput are decoupled in coded aperture imaging, the resolution and solid angle achievable with future designs will be limited primarily by manufacturing capability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1972

Fourier spectrum of beams chopped by circular apertures.

The circular apertures in the case investigated are uniformly spaced. It is assumed that modulation does not alter beam collimation and that diffraction from aperture edges can be neglected. It is also assumed that the diameter of the apertures is equal to the spacing between the trailing edge and the leading edge of successive apertures. The motion of apertures across the beam is rectilinear. Calculations have been performed for both homogeneous and bivariate normal intensity distributions. The absolute values of the first six Fourier coefficients are plotted as a function of the beam radius normalized to aperture radius.

Cohen, S. C.↗
NASA NTRS1989

Straylight analysis of an aperture shade off-set from the SIRTF optical axis

Adoption of an aperture shade whose axis is offset from the optical axis of the SIRTF telescope has been proposed by Davis (1988). Moving the high side of the asymmetric (truncated) shade away from the optical axis can equalize the barrel baffle lengths illuminated by the aperture shade and reduce the dimensions of both the barrel baffle and aperture shade. The stray-light performance of this revised design is compared to that of the SIRTF baseline design, which uses a coaxial asymmetric aperture shade. Both designs incorporate a back focal distance of 100 cm and Davis's specifications for the primary and secondary cone baffles. Adoption of an offset aperture shade for SIRTF would slightly degrade its performance but would not violate any of the stray-light requirements. The SIRTF goal of natural-background-limited observations can be met with known blacks, Class 750 mirror contamination, and either aperture shade configuration.

Dinger, Ann St. Clair↗
NASA NTRS1996

The Information Content of Interferometric Synthetic Aperture Radar: Vegetation and Underlying Surface Topography

This paper first gives a heuristic description of the sensitivity of Interferometric Synthetic Aperture Radar to vertical vegetation distributions and underlying surface topography. A parameter estimation scenario is then described in which the Interferometric Synthetic Aperture Radar cross-correlation amplitude and phase are the observations from which vegetation and surface topographic parameters are estimated. It is shown that, even in the homogeneous-layer model of the vegetation, the number of parameters needed to describe the vegetation and underlying topography exceeds the number of Interferometric Synthetic Aperture Radar observations for single-baseline, single-frequency, single-incidence-angle, single-polarization Interferometric Synthetic Aperture Radar. Using ancillary ground-truth data to compensate for the underdetermination of the parameters, forest depths are estimated from the INSAR data. A recently-analyzed multibaseline data set is also discussed and the potential for stand-alone Interferometric Synthetic Aperture Radar parameter estimation is assessed. The potential of combining the information content of Interferometric Synthetic Aperture Radar with that of infrared/optical remote sensing data is briefly discussed.

Treuhaft, Robert N.↗
NASA NTRS1995

Aperture Shield Materials Characterized and Selected for Solar Dynamic Space Power System

The aperture shield in a solar dynamic space power system is necessary to prevent thermal damage to the heat receiver should the concentrated solar radiation be accidentally or intentionally focused outside of the heat receiver aperture opening and onto the aperture shield itself. Characterization of the optical and thermal properties of candidate aperture shield materials was needed to support the joint U.S./Russian solar dynamic space power effort for Mir. The specific objective of testing performed at the NASA Lewis Research Center was to identify a high-temperature material with a low specular reflectance, a low solar absorptance, and a high spectral emittance so that during an off-pointing event, the amount of solar energy reflecting off the aperture shield would be small, the ratio of solar absorptance to spectral emittance would provide the lowest possible equilibrium temperature, and the integrity of the aperture shield would remain intact.

Source record↗
NASA NTRS2007

Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular Apertures

For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.

Aronstein, David L.↗
NASA NTRS2004

Fresnel Lenses for Wide-Aperture Optical Receivers

Wide-aperture receivers for freespace optical communication systems would utilize Fresnel lenses instead of conventional telescope lenses, according to a proposal. Fresnel lenses weigh and cost much less than conventional lenses having equal aperture widths. Plastic Fresnel lenses are commercially available in diameters up to 5 m large enough to satisfy requirements for aperture widths of the order of meters for collecting sufficient light in typical long-distance free-space optical communication systems. Fresnel lenses are not yet suitable for high-quality diffraction-limited imaging, especially in polychromatic light. However, optical communication systems utilize monochromatic light, and there is no requirement for high-quality imaging; instead, the basic requirement for an optical receiver is to collect the incoming monochromatic light over a wide aperture and concentrate the light onto a photodetector. Because of lens aberrations and diffraction, the light passing through any lens is focused to a blur circle rather than to a point. Calculations for some representative cases of wide-aperture non-diffraction-limited Fresnel lenses have shown that it should be possible to attain blur-circle diameters of less than 2 mm. Preferably, the blur-circle diameter should match the width of the photodetector. For most high-bandwidth communication applications, the required photodetector diameters would be about 1 mm. In a less-preferable case in which the blur circle was wider than a single photodetector, it would be possible to occupy the blur circle with an array of photodetectors. As an alternative to using a single large Fresnel lens, one could use an array of somewhat smaller lenses to synthesize the equivalent aperture area. Such a configuration might be preferable in a case in which a single Fresnel lens of the requisite large size would be impractical to manufacture, and the blur circle could not be made small enough. For example one could construct a square array of four 5-m-diameter Fresnel lenses to obtain the same light-collecting area as that of a single 10-m-diameter lens. In that case (see figure), the light collected by each Fresnel lens could be collimated, the collimated beams from the four Fresnel lenses could be reflected onto a common offaxis paraboloidal reflector, and the paraboloidal reflector would focus the four beams onto a single photodetector. Alternatively, detected signal from each detector behind each lens would be digitized before summing the signals.

Hemmati, Hamid↗
DOE OSTI2023

Aperture size distribution, length, and preferential location of bed-parallel veins in shale

Bed-parallel, calcite-filled veins (BPVs) are common in shale formations, and although they have been widely described in other studies, little is known about their population aperture size distribution. To address this knowledge gap, we analyzed BPV sizes in outcrops and cores from the Vaca Muerta Formation, Neuquén Basin, Argentina; in two cores from the Marcellus Formation, Appalachian Basin, northeast Pennsylvania; and in one core from the Wolfcamp Shale, Delaware Basin, West Texas. Nine out of ten aperture size populations follow a negative exponential distribution, with one following a weak power law. Bed-parallel vein size distribution and intensity vary among formations and within the same shale. We define three groups of distributions: (1) Vaca Muerta outcrops, with the highest BPV intensity and the largest BPVs (cumulative frequency of 4.9 BPVs per meter [BPVs/m] for apertures 0.265 mm to 8.7 cm); (2) Vaca Muerta cores with a similar BPV intensity overall but with no apertures wider than 1.2 cm; and (3) Vaca Muerta, Wolfcamp, and Marcellus cores with the fewest BPVs (cumulative frequency up to 0.63 BPVs/m) and very few wider than 1 cm. Aperture and length in two outcrop data sets are weakly positively correlated and follow power laws with exponents of 0.44 and 0.49. Mechanical interfaces at boundaries between different lithologies exert a strong control on BPV location, with 65–75% of observed interfaces having BPVs along them. Only 25–30% of the BPVs occur at observed material interfaces, however, and unless subtle, unobserved mechanical layering is present, other factors must also control location. BPV intensity and organic richness (TOC) from Vaca Muerta well logs are correlated in some instances but not in others, indicating TOC is not always a good proxy for BPV location or intensity. Furthermore, these findings provide useful information for modeling of hydraulic fracture treatments where BPVs may influence development of the stimulated fracture network, for example by limiting height growth.

58 GEOSCIENCES↗
DOE OSTI2025

Customizable Aperture Geometry in Metal–Organic Frameworks for Kinetic Hydrocarbon Separation

Precise control of aperture dimensions is crucial in adsorptive separations of hydrocarbons, as it directly affects key parameters such as selectivity, capacity, diffusion, and recyclability. The development of metal–organic frameworks (MOFs) has enabled the fine-tuning of local pore environments to address important hydrocarbon separations. However, customizing the aperture geometry to tune the kinetic separation performance remains challenging. Here, we deploy a mixed-linker synthesis strategy, combining long and short linkers on fcu net Zr-MOFs with equilateral triangular apertures to construct isoreticular multivariate MOFs, NU-415 and NU-416, with tailored isosceles triangular apertures suitable for the separation of hexane isomers. Sorption, liquid batch separation, and X-ray diffraction measurements demonstrate significantly improved selectivity, capacity, stability, and recyclability of NU-415 and NU-416 compared with Zr-muconate and MOF-801. Notably, both NU-415 and NU-416 achieve uptake capacities of 2.2 mmol g –1 in 1 min with an n-hexane to 2,2-dimethylbutane selectivity over 200 in an equimolar ternary mixture at ambient conditions, comparable to leading reported materials. Mechanistic studies confirm that separation performance is predominantly governed by significant kinetic differences rather than by thermodynamics. Furthermore, the successful customization of aperture geometry not only enables superior linear to monobranched hexane selectivity in NU-415 but also demonstrates the mixed-linker synthesis strategy as a promising solution for precise and predictable pore architecture control in MOFs.

Adsorption↗
DOE OSTI2025

Elliptic Aperture CCT Coils for HTS Dipole Magnets

High-temperature REBa$_{2}$Cu$_{3}$O$_{7-x}$ (REBCO) superconductors are a route to increase the field of accelerator magnets beyond the 15-16T practical limit of Nb$_{3}$Sn. REBCO cabled in a CORC geometry is a promising fit for this application, enabling the design of low inductance magnets with conductor transposition. However, the use of CORC in coils with the tight conductor bending radii typical of accelerator magnets remains a key challenge, with on-going research both on the conductor development and coil design fronts seeking to address this issue. Here, in this work we explore the tradeoffs between circular and elliptic aperture canted-cosine-theta (CCT) coils when the conductor minimum bending radius is a key consideration, concluding that aperture ellipticity is an important free parameter in the optimization of magnetically efficient CORC dipole magnets. In particular, we show that elliptic bore designs enable a regime of smaller aperture HTS coils, an important result for LTS-HTS hybrid magnets and more generally for accelerator applications benefiting from non-circular magnet apertures. To this end we present an elliptic aperture dipole design optimized for hybrid testing within the US Magnet Development Program (US-MDP) and share 77 K test results of a prototype coil which provides first experimental confirmation of the advantages.

Brouwer, L. [Lawrence Berkeley National Laboratory↗
NASA NTRS1982

Synthesis of offset dual reflector antennas transforming a given feed illumination pattern into a specified aperture distribution

The problem of transforming a given primary feed pattern into a desired aperture field distribution through two reflections by an offset dual reflector system is investigated using the concepts of geometrical optics. A numerically rigorous solution for the reflector surfaces is developed which realizes an exact aperture phase distribution and an aperture amplitude distribution that is accurate to within an arbitrarily small numerical tolerance. However, this procedure does not always yield a smooth solution, i.e., the reflector surfaces thus realized may not be continuous or their slopes may vary too rapidly. In the event of nonexistence of a numerically rigorous smooth solution, an approximate solution that enforces the smoothness of the reflector surfaces can be obtained. In the approximate solution, only the requirement for the aperture amplitude distribution is relaxed, and the condition on the aperture phase distribution is continued to be satisfied exactly.

Mittra, R.↗
NASA NTRS1986

A novel method of calculating far-field patterns of large aperture antennas

A method is described for calculation of the radiation pattern of large aperture antennas. A piece-wise linear approximation of the aperture field using overlapping pyramidal basis functions allows the radiation pattern of an aperture antenna to be calculated as though it were a two-dimensional array. The calculation of radiation pattern data versus theta and phi, suitable for 3-D or contour plot algorithms, is achieved by locating the array in the yz-plane and performing a summation over the aperture field data sampled on a square grid. A FORTRAN subroutine is provided for performing radiation pattern calculations. Numerical results are included to demonstrate the accuracy and convergence of the method. These numerical results indicate that typical accuracies of + or - 0.1 dB for Directivity, + or - dB for the 1st Sidelobe Level, and + - 2dB for the 2nd Sidelobe Level can be obtained with an aperture grid of 45x45 points and requires approximately 0.02 seconds CPU time per far-field data point on a VAX 11/750 with a floating point accelerator.

Bailey, M. C.↗