Receiver Performance and Comparison of Incoherent (bolometer) and Coherent (receiver) detection

TN (noise temperature) is defined as the temperature of a black body placed over the receiver input that would be detected at signal-to-noise of one. We have already seen the example of the quantum limit,

To right, an example of SIS receiver performance as of 2005. The mixer only noise is compared with the system noise. 2hf/k is twice the quantum limit. The limited frequency bandwidths arise because of the need to tune each receiver for maximum efficiency. At eVgap/h the photons have sufficient energy to break the Cooper pairs and the SIS performance degrades.

It is often convenient to express the flux from a source as an antenna temperature, TS, in analogy with the noise temperature. This concept is particularly useful at millimeter and longer wavelengths, where the observations are virtually always at frequencies that are in the Rayleigh Jeans regime (hv << kT). In this case, the antenna temperature is linearly related to the input flux density: where Ae is the effective area of the antenna or telescope, S is the flux density from the source, and the factor of ½ is a consequence of the sensitivity to a single polarization. The achievable signal-to-noise ratio for a coherent receiver is given in terms of antenna and system noise temperatures by the Dicke radiometer equation: where Δt is the integration time of the observation, DfIF is the IF bandwidth, and K is a constant of order one.

In the same terminology, the signal to noise with a bolometer (incoherent detector) is:

Therefore, we obtain the ratios of signal to noise achievable with the two types of system under the same measurement conditions: Suppose a bolometer is operating background limited and we compare its signal to noise on a continuum source with a heterodyne receiver operating at the quantum limit. We set the bolometer field of view at the diffraction limit, A = 2 and assume that the background is in the Rayleigh Jeans regime (i.e., thermal background at 270K observed near 1 mm). The photon incidence rate, , can be shown to be and the NEP is where TB is the equivalent blackbody temperature of the background and is the quantum efficiency of the bolometer. If we assume the bolometer is operated at 25% spectral bandwidth, D = 0.25, and that the IF bandwidth for the heterodyne receiver is 3 x 109 Hz (a typical value) then Thus, the bolometer becomes more sensitive near 2.6 x 1011 Hz and at higher frequencies, or at wavelengths shorter than about 1mm. Actually, this comparison is slightly unfair to it (since, for example, it does not have to work at the diffraction limit), so it is the detector of choice for continuum detection at wavelengths out to 2 to 3 mm. Hence, large-scale bolometer cameras have been developed for mm-wave and submm telescopes. Conversely, at wavelengths longer than a few millimeters, coherent detectors are the universal choice.

Radio Astronomy

Radio (cm-wave) Receivers: antennae

Individual photons have too little energy to detect. We treat them in terms of their electric fields. The fundamental input to a receiver is a dipole antenna. It has a very broad angular response. The pattern can be understood from the Reciprocity Theorem and simple considerations of interference. The first says that we can understand the response of an antenna to outside signals by considering the pattern it emits. The dipole than cannot emit along its length because the waves from one end interfere with those from the other. The lobes are where the interference is constructive.

More directed response can be obtained with a dipole array ; here is for a dipole only (in (b) the regions of no response are where one signal interferes with the other):

By changing the phase relation in the driving of the dipole elements, the direction of response can be changed. Now, if we take an array of dipoles, the collecting area for each dipole is given by the antenna theorem: or

For dipoles spaced at half-wavelengths, A is about 4. So at low frequencies, an array of dipoles can provide an inexpensive radio telescope.

LOFAR in Holland; low frequency array in center

• More directed response can also be obtained with a horn that feeds a dipole.

• One of these forms of antenna (dipole or horn) can be put at the focus of a paraboloid (or off a subreflector to make a highly directional detection system. Optically, the arrangement is like a Cassegrain telescope • However, the detailed description has to recognize the wave nature of the photons – for example, the antenna theorem.

• The performance of such an arrangement can be limited by signals that come from behind the paraboloid, pass just outside its edge, and are picked up directly (without reflecting off the paraboloid) by the antenna. • Taking the point of view of the Reciprocity Theorem, this is called spillover radiation. • It is reduced by tapering the response of the antenna to be greatly reduced at the edge of the paraboloid – a Gaussian response, for example (in (b) – the left side of these figures is the illumination over the paraboloid, the right side is the electric field at the antenna (dotted) and the PSF (solid). • This is apodization by another name! • c and d show the progression to an interferometer (coming after Thanksgiving)

High performance amplifiers let us inject calibration signals and increase the power in the signal before taking it to the mixer. The mixer can be a diode or transistor with a

non-linear IV curve; we do not have to put such an emphasis on mixer performance as for the mm-wave.

Mixers can be relatively conventional electronic components, such as high frequency transistors.

A metal-semiconductor field effect transistor (MESFET). The best performance uses a solid-state trick so the electrons flow in intrinsic material where their mobility is

higher – this gives a high electron mobility transistor (HEMT).

Spectrometers The IF encodes a range of input frequencies. We can decode this information and obtain a spectrum of the source with a filter bank. This is just a set of electronic filters tuned to separate frequencies. They receive the IF signal and pass only that part at their frequency. Each has a detector circuit on its output, and reading these detectors gives the spectrum.

Filter banks are expensive and inflexible – once the hardware is built, it is hard to change the frequency characteristics or other aspects of the performance. Another approach is an acousto optical spectrometer (AOS). The IF signal is coupled mechanically into a cell with a liquid – a Bragg Cell. Standing ultrasonic waves are set up in the liquid that result in a periodic variation in the refractive index. The cell acts like a volume phase holographic grating. If we build it into a spectrometer, the output (onto the CCD in this figure) encodes the spectrum basically as its Fourier Transform.

In a chirp transform spectrometer, the LO frequency is swept at a constant rate, df/dt. Thus, the heterodyne output signal for a single-frequency input signal sweeps in frequency. This stage is called the expander. A delay line, called the compressor, is used on the output. It is built to just counteract the frequency sweep, so the output for a single input frequency all occurs at one time and as a sinc function. Other input frequencies emerge at other times, so the input spectrum emerges in time series.

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A fourth approach is to use an electronic circuit that computes the autocorrelation of the IF signal:

The spectrum is recovered by Fourier transformation. Since it is not possible to let T go to infinity, an autocorrelator produces “ringing” around sharp spectral features, just as we saw for Fourier Transform Spectrometers. These artifacts can be removed by filtering to reduce the high frequency component of the signal. A “Hanning Filter” (or window) is commonly used – it is based on cosines but looks a lot like a Gaussian. Correlators can be complex and expensive, so often they are built to operate only to a small number of bits of accuracy. This is actually not as bad as it sounds.

Information retained as a Function of digital bits: 1 bit 64% 2 bits 81% 3 bits 88%

With all this effort, the beam of the GBT is 7 arcmin at 21 cm. In deep exposures it can easily become confusion limited.

Solving these problems by making a still bigger telescope is not going to work. We have to find a better way to get high resolution in the radio.

Another way to get more out of the telescope: receiver arrays

• Because of the complexity of the backend (e.g., filter bank) radio astronomers have traditionally been happy with just one receiver • This gives a high degree of spectral multiplexing (many frequencies observed at the same time) but no spatial multiplexing (measures just one position at a time). • A number of groups are developing receiver arrays – these depend on the great computer power now available to carry out the backend Functions • Here is one example: Supercam for the HHSMT

Mixer block (top) Open mixer block (center) SIS mixer and waveguide feed (lower left) SIS attached to low noise amplifier (lower right)

Power is concentrated onto the mixers with feedhorns:

Here is a particularly efficient type, called a “Winston Cone” after its inventor:

Supercam uses a single local oscillator, so the power must be divided into 64 pixels using splitters (left) inside a 8 X 8 power divider (right)

The backend spectrometer is based on a filter bank concept. It makes use of very fast analog to digital convertors (ADCs) and field programmable gate arrays (FPGAs). The ADCs digitize the IF signal at 8 bits resolution (this preserves virtually all the information). The filter bank is implemented with Fast Fourier Transforms (FFTs) on overlapping segments of the IF data stream. The architecture is optimized for speed by dividing the data stream into blocks and making the FFTs operate on them with the most efficient spacing (termed ployphase). The electronics are surprisingly compact (left). Supercam goes onto the SMT as to the right and is currently going to visit APEX in Chile (altitude 5000 meters).