EMS Logo
Engineering Metrology Services

Return to EMS Publications Page


Prepared for The Proceedings of the IEEE Special Issue on the Design and Instrumentation of Antennas for Deep-Space Telecommunications and Radio Astronomy

Prepared by:

Michael J. Brenner, Engineering Metrology Services
Joel Ellder, Chalmers Technical University
Mehdi Zarghamee, Simpson, Gumpertz and Heger, Inc.


A 20.1 meter diameter radome enclosed radio telescope, installed at the Onsala Space Observatory (OSO) near Gothenberg, Sweden in 1975, was upgraded in 1992 for improved operation at 115 GHz, increasing the system aperture efficiency from 20 to 40 percent at this higher frequency. Electrical gain measurements confirm geometric optics predictions of efficiency and improved antenna patterns.

The upgrade included replacement of the two inner reflector panel rows with modern 31 micron panels, stiffening the reflector backstructure based on finite element structural analysis for a measured rms gravity deformation of 59 microns in the 25 to 70 degrees elevation range, and optical alignment of the reflector surface to 58 microns rms accuracy. This alignment accuracy of approximately 1/345,000 of the reflector diameter was accomplished with an electronic angle-measuring theodolite and digital radial strap gauges. Data was downloaded in real time to an on-line portable computer performing surface metrology calculations.

Graphical data are presented that compare computer predictions of reflector backstructure gravity deformations to optical measurements, which proved crucial in achieving the stringent alignment accuracies. Measured antenna efficiency data before and after the upgrade are included.

Keywords: radio telescope, millimeter wavelength instrument, upgrade, finite element analysis, reflector surface alignment

A number of high quality antennas were built from 1961 through 1975 for operation at low centimeter and high millimeter wavelengths (10 to 44 GHz). With the expanding interest in low millimeter and submillimeter radio astronomy (85 to 350 GHz), it is often economical to upgrade an existing instrument.

One such radio telescope is the 20.1 meter Onsala Space Observatory near Gothenberg, Sweden, shown in Figure 1, and as upgraded in Figure 2. The radome-enclosed Cassegrain antenna was built in 1975 for highly efficient operation up to 44 GHz [1]. Since that time, the antenna has operated at better than 50 percent aperture efficiency at this frequency, with an rms surface accuracy of about 230 microns. 

Side cut-away elevation of Onsala  telescope

In 1992, the system was upgraded to obtain a measured system aperture efficiency of 41 percent at 110 GHz. The upgrade included the following changes to the antenna:

· Replace the most highly illuminated reflector panels.

· Add diagonal members to the backstructure to stiffen it and improve the homology of the gravity deformations.

· Preload the critical backstructure structural connections to eliminate sources of nonlinearity and hysteresis.

· Stiffen the pedestal to improve the operation of the thermal expansion fittings.

· Improve the reflector panel alignment.

The work included a detailed finite element analysis, design of an efficient and cost-effective backstructure stiffening technique, and manufacture, installation and alignment of 31 micron rms reflector panels.


When the 20.1 meter diameter Onsala radio telescope was built it was the largest millimeter wavelength telescope in the world [1]. A number of new generation telescopes have been built in the years since 1975 to explore the millimeter and submillimeter wave spectra, including SEST [2], which is the Swedish southern hemisphere complement to the Onsala, Sweden telescope. These instruments typically have system aperture efficiencies ranging from 50 to 58 percent at 115 GHz [2, 3].

The original purchase specification for the antenna required an rms surface accuracy of 250 microns at 60 degrees elevation, degrading to not greater than 350 microns between 0 and 90 degrees elevation. As described below, the actual as-built rms surface accuracy was 200-230 microns over the full range of elevation motion, resulting in a system aperture efficiency of approximately 20 percent at 115 GHz.

Since 1975, numerous technical advancements have been made, resulting in a current generation of antennas with rms surface accuracies in the 50 to 150 microns range [4, 5]. A thorough review of the antenna performance as described below indicated that system aperature efficiency could be raised from 20 to 40 percent at 115 GHz.


A thorough understanding of the telescope performance history and the sources of major gain losses was crucial in selecting the best upgrade strategy. Table 1 is a surface accuracy and gain budget for the antenna as configured both before and after the upgrade. The relationship between rms surface errors and efficiency was defined by Ruze [6].


AT 115 GHz
AT 115 GHz
RMS Acc'y, mm
Gain Loss, dB
RMS Acc'y, mm
Gain Loss, dB
Primary Surface Panel Manufac-turing Acc'y
Subreflector Surface Manufacturing Acc'y
Surface Alignment
Backstructure Gravity Deformation
Backstructure Thermal Deformation
Quadrapod/Subreflector Blockage
The antenna was measured holographically in 1983 at 24 degrees elevation yielding an overall rms surface accuracy of 253 microns, and again in 1990 at 15 degrees elevation, with an accuracy of 268 microns [7]. The reflector surface was extensively measured optically in 1976, 1981 and 1989, using a single theodolite at the primary vertex for target angular positions and a precision metal tape for radial position measurements [8], indicating an rms surface accuracy of 220 microns. These measurements were taken with the antenna at zenith. Theodolite measurements at 45 degrees elevation showed a similar level of accuracy.

The primary surface panels and the subreflector were measured in 1974 on a three axis Coordinate Measuring Machine (CMM). The rms surface accuracies were 114 and 48 microns, respectively [9, 10].

A structural deflection analysis of the reflector backstructure predicted an rms surface gravity deformation of 178 microns between 20 and 90 degrees elevation for a reflector aligned for at 60 degrees elevation and active subreflector motion to optimize antenna gain at all elevation angles [11]. A value of 140 microns gravity deformation is used in Table 1 when the analytical predictions are taken in the context of the holographic results and other data.

The thermal deformations of the backstructure within the radome were calculated [12], indicating an rms surface error of 124 microns for a 1.1 degree C gradient across the depth of the backstructure. Ratioing this value based on measurements at OSO of gradients less than 0.5 deg C gives an rms thermal error of 51 microns. This value was not changed by the upgrade.

Alignment accuracy is limited by that of the measurement method. The rms measurement accuracy for previous theodolite surveys was estimated at 55 microns [8]. Analysis of the theodolite measurement procedure described here indicates a measurement accuracy of 1/400,000 of the reflector diameter, or 50 microns. Among recorded theodolite approaches for measuring reflector antennas, this accuracy level is matched only by the IRAM 30 meter radio telescope [13]. Both the theodolite and holography data at various elevation angles [7, 8] indicate reflector panel misalignment. Based on these measurements, the alignment accuracy before the upgrade shown in Table 1 is 2 times the measurement accuracy, or 110 microns.

The subreflector and quadrapod blockage was calculated based on the geometric and physical optics technique described by Ruze [14]. The radome losses are based on extensive analysis and testing, including the effects of frame blockage, membrane absorption, and illumination taper.

A series of measurements of the beam shape to understand sidelobe performance were performed, indicating that the antenna had a variable elevation sidelobe at around 3 millimeters wavelength, probably due to a primary surface distortion.


The aluminum reflector backstructure comprises 12 radial ribs and 3 rows of circumferential intercostals as shown in Figures 2 and 3. The ribs and two outer intercostal rows are rivetted and bonded sheet metal box beams nominally 1372 mm (54 inches) deep by 300 mm (12 inches) wide. Box beam skin thicknesses vary from 1.5 to 6.4 mm (0.06 to 0.25 inches). The inner circumferential intercostal ring is a substantial box beam called the torque box, and is designed to spread the forces from the antenna support points into the structure. The torque box sheet metal walls are nominally 10 mm (0.38 inch) thick. Structural bulkheads are built into the interior of the radial ribs at the locations of intersection with the intercostals in order to maintain continuity in the circumferential structural load path.

Figure 2  The upgraded antenna, rear view Figure 3  Backstructure stiffening
The antenna was modified as described below to meet the performance requirements:

1. The two inner rows of reflector panels with aggregate rms manufacturing accuracies of 121 microns were replaced with modern 31 micron panels. The outer 100 micron panels were not replaced.

2. The primary reflector backstructure was stiffened by the addition of diagonal members between radial ribs and by preloading the rib-to-intercostal connections as shown in Figure 3. The diagonals fill the open backstructure bays defined by the radial ribs and circumferential intercostals. By changing the structural action from that of a frame to a truss, the magnitude of face-side (horizon pointing) deformations is significantly reduced.

Preloading of the rib to intercostal connection stiffens the joint while ensuring linear structural response. This is critical because the finite element structural analysis and geometric optics post processing are based on a fully linear structure. Figure 3 shows a typical joint detail in the as-built original configuration, the next generation design, and the upgraded configuration. In the original configuration, the load path for tensile forces through the structural bulkhead followed an indirect route through the rivet, acting as a flexible leaf spring. The load path for compressive forces is much shorter, completely bypassing the rivet. This difference between the tension and compression load paths is a nonlinearity, compromising the accuracy of all structural analyses. The next generation design uses special extruded joint members in which the pretension in the bolts is used to precompress the joint. The bolt torque is selected to provide a precompression greater than the maximum possible tension at the joint, ensuring a direct load path under all operating conditions.

The upgraded configuration represented at the bottom of Figure 3 shows how the structural improvements of the next generation design are integrated into the existing structure, while eliminating the necessity of reworking the interior of the closed box beams. The pretensioned threaded rods, spaced on approximately 100 mm centers, extend through the full width of the radial rib, causing an equal precompression of the internal bulkhead, and thus providing the required preload at the base of the angle. In the field, the nuts were torqued to provide the required joint preload while preventing compression buckling of the bulkhead.

3. The pedestal pickup arm connection was stiffened to control the slippage at the reflector support thermal expansion fittings.

4. The primary reflector was aligned to optimize performance at 49.28 degrees elevation.


To predict the gravity deformations of the modified antenna, a NASTRAN finite element model of the backstructure was developed, consisting of idealized beam elements representing ribs, intercostals and subreflector support spars. These beam elements are positioned at the centerline of the members which they represent. The torque box is idealized as plate elements connected by rigid, weightless standoffs to the beam idealizations of the ribs. Diagonals are assumed to provide only axial stiffness, and to span the distance between the nodes at rib centerlines with an offset equal to one-half of the rib depth. The member section properties have been calculated based on the actual sections. The reflector panel stiffness is considered negligible, but the panel-induced forces and moments are applied to the structural nodes at the centerline of the ribs and intercostals.

The flexibility of the intercostal-to-rib connections is modelled by computing a knock-down factor for the actual stiffness of the intercostals. The knock-down factor is computed using a finite element model of the rib walls, the intercostal walls, the bulkhead inside the rib, and the connecting angles as shown in Figure 3.

The spars were assumed to be either pinned or fixed at a point that is rigidly connected to the ribs. Both options were considered due to the uncertainty in the actual behavior of the connection. The true behavior is most likely between the pinned and fixed conditions considered.

The model computed the deflections and rotations of the structural nodes, located at the centerlines of the ribs and intercostals. For every structural node, a point was defined on the primary surface such that a line normal to the paraboloid passed through the surface point and the corresponding structural node. The nodal displacements and rotations were used to compute the components of the surface deformations of the primary reflector, taking into account the offset of the surface from the structural nodes.

The calculated nodal deformations due to face-up (zenith) and face-side (horizon) gravity loading can be combined to compute the gravity deformation at each surface point and the overall rms gravity deformations at any elevation angle as shown below:

d(E) = du(sin E - sin E0) + ds(cos E - cos E0)

RMS(E) = [RMSu2(sin E - sin E0)2 + RMSs2(cos E - cos E0)2] 1/2

where d is the RF-half path length change after bestfitting, subscripts u and s refer to face-up and face-side deformations, E is the elevation angle of interest and E0 is the elevation angle at which the reflector is a perfect paraboloid. By equating the rms(E) at 25 and 70 degrees elevation, E0 was determined to be 49.28 degrees.
Based on the surface coordinates, the optimal subreflector position is determined by first bestfitting a plane through the calculated near-field phase front and then defining the axial and lateral subreflector position which minimizes the residual rms path length errors, maximizing the antenna gain as a function of elevation angle [15, 16]. 

The results plotted in Figure 4 show that the effective surface rms gravity deformation of the antenna, and therefore overall system performance, is highly dependent on proper lateral subreflector adjustment. In fact, a significant portion of the primary backstructure deformation can be corrected by a lateral subreflector translation.


Figure 4  Reflector RMS accuracy aligned at 48.28 degrees



The most accurate surface measurement techniques for enclosed antennas are optical surveys [13]. Even the best corrections for the radome effects on the accuracy of holographic measurements result in a measurement accuracy of 1/305,000 of the antenna diameter [17], which is not adequate for this upgrade. In general, holographic antenna measurements for radome-enclosed systems do not meet this accuracy level.

The selected reflector alignment technique is an improvement on the traditional theodolite/tape method [8, 18]. In principle, measurement and mathematical compensation replace enforcement of precise locations of the theodolite and panels, simplifying and speeding up the surface measurement and alignment process.

The reflector panels are fabricated from laser-cut flat sheet aluminum skins 1 mm thick. The edges, inner and outer tooling holes and target holes are all placed in the skin to a position tolerance of 125 microns. The flat skin coordinates are mathematically transformed from the flat sheet system first into the local panel coordinate system, and then into global antenna coordinates. Each panel has a tooling hole near the inboard and outboard end, nominally 63 mm from the ends of the panels. Additionally, holes for mounting plastic alignment targets are placed directly above each of the panel adjustment screws. The inner reference for the panel radial position is a groove nominally 1500 mm in diameter machined into a permanent primary vertex reference ring.

The targets were measured during the thermally stable hours from 2300 to 0300 hours using an electronic Wild T2002 theodolite as shown schematically in Figure 5. The angle data is downloaded on command to a portable computer via an RS-232 interface. All reflector metrology calculations are performed in real time by custom software. The panel radial positions are measured over the nominal 125 mm span between tooling holes with a custom micrometer gauge as shown in Figure 5, and the data is input into the alignment software for each of the 120 surface panels.

Figure 5  Reflector measurement setup
It is critical to know the position of the theodolite with respect to the nominal vertex of the reflector. While a theodolite tilt is identical to a rigid body rotation of the primary, and thus not a critical measurement [18], an uncorrected lateral dislocation of the instrument can induce surface alignment errors. The theodolite location is determined by software calculations based on measurements of a target bar as shown in Figure 5 at four locations on the vertex ring. The theodolite coordinates calculated numerically, where the instrument lateral coordinates and tilts can each be calculated 4 times, and the height 8 times. These data are presented to the operator for review and acceptance, and the average values are used in subsequent geometry calculations.

The software calculates the theoretical coordinates and theodolite angles of each of the 764 surface targets based on the known theodolite coordinates, local panel target locations, and measured panel radial positions. When the measured theodolite target angles are downloaded into the computer, the differences between the theoretical and actual surface coordinates at each target are calculated. The actual surface coordinate data are used in a number of ways. Deviations normal to the surface are used for panel adjustment data, while the projections of the normal errors onto the boresight axis are the half path length errors which are used to calculate rms accuracy values.

Theodolite measurements can be performed at any elevation angle, but are most reliable with the reflector at zenith, where the operator can comfortably stand for the 3 to 4 hours required to take the data. However, the elevation angle for optimal performance is 49.28 degrees, referred to as the bias rigged angle. The theoretical gravity deformations as the antenna travels from the bias rigged angle to the zenith position are determined by structural analysis as described above. Using the equations shown previously, the normal bias superimposed on desired the paraboloidal shape is calculated as shown below:

normal bias = Nu [1 - sin(49.28 deg)] - Ns cos(49.28 deg)


normal bias = offset normal to the reflector surface

Nu = face-up normal deformation

Ns = face-side normal deformation

Theoretical surfaces are transformed to bestfit the measured surfaces using standard multiple degree of freedom least squares linear techniques, including three translations, two rotations and calculation of a bestfit focal length.


The measurement technique used here is unique in its ability to directly measure the gravity deformations of the structure. As a check on the analytical predictions, the bias rig data were directly measured. WIth the antenna pointed at zenith and immediately after at 49.28 degrees, the panel radial positions, theodolite location, and target angles were measured. At zenith the full complement of 764 targets were used, while at the lower angle a representative sample of 96 points proved sufficiently dense. After removing the constant and linear terms from the residual path length errors, the difference between the two data sets converted from path length to surface normal errors is a true measure of the bias rigging data. These difference measurements were taken four times during the reflector alignment process. By averaging the results from four independent measurements, the reliability of the data is improved. Because they are relative measurements, the accuracy of reflector alignment at the time of the measurement is not relevant.

Figure 6 contains four contour plots of the reflector surface showing differences normal to the paraboloid in mils. Figure 6a is the theoretical normal bias data based on the finite element analysis. Figure 6b shows the average of the four theodolite measurements of the normal bias. Figure 6c shows the required additions to the theoretical normal biases. This correction to the theoretical normal deformation was computed at the site during the surface alignment process by comparing the contour of the average of the four measurements (6b) with those predicted by the model (6a). Figure 6d is the sum of the data from 6a and 6c, and closely matches 6b. The updating of the theoretical normal bias values based on actual field measurements is necessary to ensure that a true paraboloid will exist 49.28 degrees elevation.

It is interesting to note that the pattern of the added normal biases of Figure 6c is nearly identical to that produced by a lateral subreflector shift [15], indicating that the final performance of this antenna would not have been significantly affected if the theoretical normal bias data had been used without modification.

The reflector surface targets were aligned to the updated biased coordinates. As the alignment progressed, the deviations from the bestfit paraboloid were plotted for the measurements at 49.28 degrees. A final check on the accuracy of the updated bias data was the plot of these deviations. As the alignment progressed with progressively improving bias rig data, these plots showed more randomness and less of the gravity deformation pattern shown in Figure 6.

Figure 6 Theoretical measured and updated bias rig data
Figure 6 Theoretical measured and updated bias rig data
Table 2 is a summary of the reflector surface rms half path length alignment accuracy based on the final theodolite measurement. The results show that the reflector was aligned with respect to the surface biased for 49.28 degrees elevation to an rms accuracy of 58 microns. This is a measure of the error which can be expected at the optimal elevation angle. In the zenith position, the rms alignment accuracy is 376 and 145 microns for 3 and 6 degree of freedom bestfitting, respectively. In thisparaboloidal bestfitting, the first 3 degrees of freedom eliminate the axial offsets and axis tilts. The final 3 degrees of freedom shift the primary laterally and optimize the focal length. This is an approximation of the benefits which result from optimizing antenna optics via active subreflector alignment [15]. When the actual surface coordinate data were used in the subreflector optimization routine, the rms of the half path length errors improved to 130 microns.


Table 1 shows the half path length rms errors, gain losses and efficiencies from the primary and secondary reflectors, as well as the losses from the subreflector support quadrapod, radome and feed. The relationships between rms surface accuracy and gain loss and efficiency assume a random distribution of surface errors [6].

The 24 inner panels and 48 intermediate panels were replaced, improving the aggregate rms panel manufacturing accuracy of the replaced panels from 121 to 31 microns. The rms accuracy of the existing outer panel row is 100 microns. When combined in aggregate with the new panels, the new aggregate panel manufacturing rms accuracy is 69 microns.

The primary surface alignment rms accuracy is 58 microns as described above and shown in Table 1. This accuracy value of 1/345,000 of the reflector diameter appears to be the best possible for this antenna system [13].

Analysis of the reflector surface data collected at zenith provides information about the gravity deformation of the structure. The fully optimized reflector rms accuracy with the antenna at zenith is 130 microns, as described above. This value combines in an rss (root sum square) manner the two independent effects of alignment error and gravity deformation. Removing the known alignment error leaves a zenith rms gravity deformation of 116 microns.

This measured value is 2.1 times the analytical prediction for rms gravity surface deformation at zenith of 56 microns shown in Figure 6. Applying the same multiplication factor to the 28 microns predicted rms gravity deformation at 70 degrees elevation provides a realistic estimate of the rms gravity deformation at this look angle. This value of 59 microns appears in Table 1.


Preliminary measurement of the electromagnetic performance of the upgraded radio telescope was accomplished at 86.2 and 110.2 GHz using Venus, Jupiter, the Moon and SiO maser sources. After confirming that the subreflector was properly illuminated, the optimal subreflector position was determined. The subreflector was positioned by updating the old subreflector position based on the 6 degree of freedom paraboloidal bestfit parameters from the new primary surface measurements, and the optimal subreflector position along the boresight axis was determined by test.

The measured Half Power Beam Width (HPBW) at the two frequencies was approximately

HPBW = 1.16 l/D

 This gives the following approximate relationship between the aperture efficiency (Aeff) and the beam efficiency (Beff) [19]:

Beff = 1.22 Aeff

 Table 2 shows results of initial measurements of the actual antenna system efficiency with the antenna at 43 degrees elevation. The Table shows the results in terms of both aperture efficiency and beam efficiency.


The observed aperture efficiency 110.2 GHz shown in Table 2 is 41 percent, which is close to the prediction of 41.9 percent from Table 1 at 115 GHz. However, the observed efficiency value from Table 2 must be adjusted in two ways to provide a true comparison to the predicted value. First, the operating frequency increase must be accounted for in the effects of reflector surface errors. Second, the effects of the measured gravity deformation must be added.

In order to account for the frequency difference, the effects of the radome, subreflector support and feed as shown in Table 1 must first be removed from the observed 41 percent efficiency at 110.2 GHz, increasing it to 66.8 percent, corresponding to an overall rms surface error of 138 microns. These observations took place near the optimum elevation angle, so the rms gravity deformation from Table 1 of 59 microns must be added, increasing the overall rms surface accuracy to 149 microns, which is slightly higher than the Table 1 value of 128 microns. Converting this surface accuracy to efficiency at 115 GHz and replacing the blockage and the radome and feed effects results in an equivalent observed efficiency of 36.6 percent, which is 5.2 percent below the prediction.

At the time of these preliminary RF measurements, neither the antenna tracking servo loop nor the high frequency receiver noise properties were fully calibrated for this high frequency operation, and may have contributed to these measurement differences. A more complete measurement and data analysis will be carried out when the antenna tracking and receivers are in their final "state of the art," and are expected to indicate improved performance. Considering these factors, the predicted and observed telescope performance are in good agreement.


It is possible to significantly upgrade the performance of a well-built millimeter wavelength antenna. Fundamental to success are a knowledgeable and dedicated antenna operations staff, the use of modern structural design and analysis techniques, knowledge of both theoretical and practical antenna optics optimization processes, a manufacturing capability for highly accurate reflector components, and up-to-date antenna measurement and data analysis techniques.


[1] D. H. Menzel, "A New Radio Telescope for Sweden", Sky and Telescope, vol. 52, no. 4, October 1976.

[2] R. S. Booth, G. Delgado, M. Hagström, L. E. B. Johansson, D. C. Murphy, M. Oldberg, N. D. Whyborn, A. Greve, B. Hansson, C. O. Lindström, A. Rydberg, "The Swedish-ESO Submillimetre Telescope (SEST)", Astronomy and Astrophysics, vol. 216, pp. 315-324, 1989.

[3] J. W. M. Baars, B. G. Hooghoudt, P. G. Mezger, M. J. de Jonge, "The IRAM 30-m Millimeter Radio Telescope on Pico Veleta, Spain", Astronomy and Astrophysics, vol. 175, pp. 319-326, 1987.

[4] M. J. Brenner, J. Antebi, D. Dusenberry, "The Design and Structural Analysis of a Large Outdoor Compact Range Reflector", Trans. of the Antenna Measurements Techniques Association (AMTA), 1990.

[5] M. J. Brenner, H. Hartwell, R. Abbott, P. Gustafson, "The Design, Fabrication and Surface Alignment of a Large Blended Rolled Edge Compact Range Reflector", Trans. of the Antenna Measurements Techniques Association (AMTA), 1991.

[6] J. Ruze, "Antenna Tolerance Theory - A Review", Proc. IEEE, vol. 54, pp. 633-640, 1966.

[7] N. Whyborn, L. Ellder, D. Morris, "Holography of Onsala 20M Telescope", Internal Report of the Onsala Space Observatory, July 1990.

[8] A. Greve, J. Ellder, L. E. B. Johansson, B. Hansson, "Theodolite-Tape Measurements of the Onsala 20-Meter Reflector", Internal Report of the Onsala Space Observatory, 1989.

[9] R. D'Amato, "Surface Accuracy of 66-Ft. Diameter Reflector Panels",Technical Document D75-20, 1975.

[10] R. D'Amato, "Subreflector for 66-Ft. Diameter Antenna", Technical Document D75-18, 1975.

[11] A. R. Raab, "Deflection Analysis of the Final Design of a 66-Foot Diameter Steerable Antenna", Technical Document D74-37, 1974.

[12] M. S. Zarghamee, "Design and Analysis for 60-ft Antenna Tracking System (ATS) for Midway Research Center (MRC); Predicting Antenna Performance Based on Detailed Structural Model of the Antenna", Memorandum from author, 21 August, 1987.

[13] A. Greve, "Reflector Surface Measurements of the IRAM 30-m Radio Telescope", International Journal of Infrared and Millimeter Waves, vol. 7, no. 1, 1966.

[14] J. Ruze, "Antenna Gain Loss Due to Feed Support Blockage", CAMROC Technical Memo no. 19, 10 February, 1967.

[15] M. S. Zarghamee, J. A. Antebi, "Surface Accuracy of Cassegrain Antennas,", IEEE Transactions on Antennas and Propagation, vol. AP-33, no. 8, pp. 828-837, August 1985.

[16] M. S. Zarghamee, "Peak Gain of a Cassegrain Antenna with Secondary Position Adjustment," IEEE Transactions on Antennas and Propagation, vol. AP-30, no. 6, pp. 1228-1233, November 1982.

[17] A. E. E. Rogers, R. Barvainis, P. J. Charpentier, B. E. Corey, "Corrections for the Effects of a Radome on Antenna Surface Measurements Made by Microwave Holography", IEEE Transactions on Antennas and Propagation, vol. 41, no. 1, pp. 77-84, January, 1993.

[18] M. J. Kesteven, B. F. Parsons, D. E. Yabsley, "Antenna Reflector Metrology: The Australia Telescope Experience", IEEE Transactions on Antennas and Propagation, vol. 36, no. 10, October 1988.

[19] M. A. Gordon, J. W. M. Baars, W. J. Cocke, "Observation of Radio Lines of Unresolved Sources.....", Astronomy and Astrophysics, vol. 264, pp. 337-344, 1992.

EMS Home Page | Experience | Equipment | Software | Publications | Current | Contact EMS