Emergence of Millimetre-Wavelength Telescopes

Abstract

As mentioned in Chap. 2, a major cause of frustration to the radio astronomer is the extremely poor angular resolution compared to what is provided in the optical domain. One way to overcome this handicap is the use of interferometers or synthesis telescopes. However, there also remained the desire to extend the frequency range of single reflectors to very high frequencies with as large a size as possible, which would both improve the resolution and widen the available window in the electromagnetic spectrum. It led to activities in the development of mm-wavelength detectors and the realisation of reflector antennas capable of observing at wavelengths as short as 1 mm. This posed new challenges to the structural design engineer and to manufacturing, particularly of highly accurate reflector surface panels. We describe the results of these efforts in this and the following chapter by example of some of the telescopes dedicated to the millimetre- and submillimetre-wavelength range.

Addendum: Thermal Effects and Their Control

The thermal behaviour of the antenna structure is determined by the interaction of radiation, both onto and from the structure, convection by the wind and by forced air circulation inside a closed structure and conduction that depends on the thermal time constant of the structural members. The thermal balance between radiation, convection and conduction determines the actual temperature of the telescope. We discuss here the basic relations governing the thermal balance of the telescope. From these we can build a thermal model of the structure that will help us design a thermal control system to limit the thermal deformations to the specified values. This system may take the form of an outside cladding with thermal insulation and possibly an additional air circulating system. Contrary to the static elastic behaviour of the structure, thermal effects are inherently time dependent. We summarise their role in the actual situation of a telescope operating under the influence of the environmental effects such as solar radiation and wind.

The daily variation in temperature is caused mainly by solar radiation. The effect of radiation on the thermal balance of the telescope structure is dependent on the emission and absorption characteristics of the material. These parameters depend on the temperature of the radiating body. Their values can be influenced by the treatment of the outer surfaces of the structure.

We distinguish three temperature regimes along with the wavelength of maximum radiated power:

• 1. The Sun at about 5800 K with its maximum at visible wavelengths (0.5 μm),

• 2. The cold sky in the range of 50–200 K, with a maximum in the far-infrared (30–60 μm),

• 3. The telescope at ambient temperature of the site, in the range of −30 to +30 °C, equivalent to 243–303 K, with its maximum in the infrared near 10 μm.

The energy balance of a surface under solar radiation requires that the absorbed solar power in visible light is equal to that radiated by the surface at infrared wavelength. The ratio of the absorption and emission coefficients for solar radiation and ambient surface temperature determines the heating of a surface under sunshine illumination. Note that at a given temperature the emission coefficient of a material is equal to its absorption coefficient (Kirchhoff’s Law). In Table 5.4, we reproduce from Höfling (1978) typical values for the emission coefficients of treated surfaces used on telescopes. Here “aged surface” means a surface that has been exposed to the environment for a considerable time.

Table 5.4 Emission coefficients of treated telescope surfaces

Inspecting the table we notice that colour-painted surfaces behave closely to being black. Clear metallic surfaces have small emission coefficients; they become very hot under sunshine. The white painted surface absorbs little solar heat but radiates strongly in the infrared. It can get colder than the ambient air even during sunshine!

The effects of radiation are counteracted by convection, that is, the effect of heat transport by the moving air (wind) along the surface of a body. It is a complicated physical process that is dependent on the shape and surface characteristics of the body as well as the velocity and viscosity of the air. Fortunately, it is possible to perform calculations of the convective heat exchange with the use of a few characteristic parameters without complicated mathematics. The convective heat transfer between a solid body and a moving surrounding gas or fluid is proportional to the Nusselt number that is dependent on the size of the body and the speed of the wind as well as the Reynolds number , which characterises the state of turbulence of the air flow.

Calculation of Thermal Load Cases

With the knowledge of the emission coefficients of the materials and applying the convective parameters, we can design realistic measures to diminish temperature differentials in the telescope. The thermal exchanges in a reflector with backup structure (BUS) with attached insulation are sketched in Fig. 5.34. It depicts a schematic of all heat effects from the reflector surface at the top through insulation, the BUS containing structure and air and outside insulation. The general expression for the thermal balance at the surface of an antenna, both the reflector proper or a possible cladding around the remainder of the structure, can be stated as:

Fig. 5.34

Thermal effects in a reflector structure with insulation. Colour scheme: blue convection, pink radiation of structure at ambient temperature, yellow solar radiation input and grey sky radiation input. W is wind on reflector and inside the BUS

The sum of radiative input from Sun and sky equals output from surface by radiation and convection . Calculating the thermal balances at the various transitions between material and air, we can derive the equilibrium temperatures at the surfaces as a function of the wind velocity.

We present now the result for a few cases that apply to the MRT and LMT . The plots show the temperature change at a particular surface as function of wind speed with structural features (such as insulation and surface treatment) as parameter. We consider two different surface treatments that are common in reflector antennas (see Table 5.4):

• “Aged” white paint with α_sol = 0.50 and ε_amb = 0.95 for outside reflector or cladding surface,

• “Aged” treated aluminium with α_sol = 0.15 and ε_amb = 0.05 for both outside and inside surface.

Surface Temperature of a Free Versus Perfectly Insulated Reflector

Choosing a simple but instructive case we first consider a metal surface in two situations:

• 1. A metal plate supported above the earth and facing the Sun.

• 2. A similar plate but perfectly insulated on the rear side. It is the top part of Fig. 5.34 (blue-grey) without any conduction through the insulation. Thus, no heat energy is exchanged at the inner side of the surface. The solutions for the two cases are shown in Fig. 5.35 in dashed lines for the free plate and full lines for the insulated plate. Only the front side of the panel is painted white.

Fig. 5.35

Surface temperature of an aluminium panel with (full lines) and without (dashed lines) backside insulation for the situation SUN and NIGHT. Panel is painted (white) on front side or bare (alu)

We note the following features. With solar input and very low wind speed, the insulated bare aluminium panel heats to a very high temperature near 120 °C. When the insulation is removed and heat exchange takes place also on the backside of the panel, the heating is limited to about 55 °C (red). With the painted panel, the radiation from the surface dominates the heat balance resulting in a lower maximum temperature and a small dependence on wind velocity (blue). At night, the dominant effect is radiation and the painted panel cools to low temperatures, well below freezing (green). This effect is increased by the presence of the insulation on the backside. The aluminium surface has a very low emission coefficient and remains essentially at the assumed ambient temperature of 0 °C (pink).

Temperature of Insulated Reflector with Open or Controlled BUS

We now take a more realistic case of a “panel” consisting of a metal outer plate to which insulating material of a finite thickness has been attached on the inside. This could be the actual reflector surface but also an insulating cladding around the backup structure (BUS). We now have a small heat conduction through the insulation in addition to the radiative and convective heat exchange.

We assume first that the BUS of the antenna is “open”, exposed to the wind and at ambient temperature (no cladding). The results of the calculations for the panel outside temperature are displayed in Fig. 5.36 in full lines (open BUS). They are similar to the case of the perfectly insulated panel of Fig. 5.35.

Fig. 5.36

The outside reflector temperature as a function of wind speed. The metal reflector panels are covered on the inside with a layer of insulation. The panels are connected to an open BUS without cladding (full lines) or to a completely enclosed and insulated BUS at a constant temperature of 10 °C (dashed lines)

The MRT , described above, has a completely enclosed and insulated BUS with an active system to control its temperature, independent of the ambient air temperature. Now the inside of the insulation of both cladding and panel will experience convective heat exchange with the BUS and enclosed air at a constant temperature. The resulting outside temperature of the panel is shown in Fig. 5.36 as dashed lines. As the figure shows, the control of the BUS temperature is not relevant for the control of the outside panel temperature. Its purpose it to keep the BUS temperature on the level of the yoke to avoid large-scale deformation of the BUS.

The temperature on the inside of the insulation is determined by the balance of the heat transported through the insulation and the convective transport from the inside, assisted by the inside airflow (see Fig. 5.34). The BUS temperature is set to 10 °C. The results for this case are shown in Fig. 5.37.

Fig. 5.37

The temperature on the inside of the insulation as a function of wind speed for the same layout as in figure. The BUS is kept at 10 °C by the control system

Inspecting the three foregoing figures, we can draw the following conclusions:

• 1. Under solar illumination, the outside temperature of the realistic panel heats less at low wind speed than in the first example of perfect insulation because of the finite conduction of heat through the insulation.

• 2. We see a small influence of the controlled, constant temperature of the BUS on the outside temperature both at day (sun) and night at low wind velocities.

• 3. In the case of the controlled BUS, it is not surprising that the inner surface of the insulation is barely dependent on the wind speed. In the BUS, the air speed is fixed at 2 m/s.

• 4. Because the aluminium surface of the insulation panel has a low emission and absorption coefficient, it settles at night between T_amb and T_BUS, here at 8 °C. The strong cooling of the white outside at night causes the inside of the insulation to be below the BUS temperature of 10 °C (green dashed). This indicates that the BUS is being heated to keep it at its prescribed temperature.

• 5. The inside temperature of both a white and aluminium surface heats to well above the BUS temperature of 10 °C under sunshine. This implies that during daytime the BUS must be cooled to retain its temperature.

A summary plot for the MRT is shown in Fig. 5.18 of Sect. 5.3.6.