6. GREAT

6.1 Specifications

6.1.1 Instrument Overview

The German REceiver for Astronomy at Terahertz Frequencies (GREAT) is a modular heterodyne instrument with multiple configurations (see below) that provide high resolution spectra (up to R = 108) in several frequency windows between 0.4900–4.7448 THz.

The front-end unit consists of two independent dewars that operate simultaneously.

One dewar always contains the following channel:

upGREAT High Frequency Array (HFA)
The HFA is a 7-pixel array arranged with 6 pixels in a hexagonal geometry around a central pixel. The local oscillator is a Quantum Cascade Laser with a narrow tuning range limited to the [OI] 63 µm frequency of 4.74477749 THz (with a tuning range of roughly + 250 km/s to -100 km/s in LSR velocity).

The other dewar contains one of the two following channels which are usually exchanged part way through a flight series:

upGREAT Low Frequency Array (LFA)
The LFA is a 14-pixel array with two polarizations (Horizontal and Vertical with 7 pixels each) with 6 pixels arranged in a hexagonal pattern around the central pixel. Both polarizations of the array (LFAH and LFAV) can be tuned to one simultaneous or two independent frequencies in the 1.835-2.007 THz range. The pixels for both polarizations are spatially co-aligned, so tuning both polarizations to the same frequency is equivalent to doubling the exposure time. Tuning the LFA polarizations to two independent frequencies is offered on a best effort basis. The [OI] 145 µm line can can only be observed in V polarization, which has an additional tuning range from 2.060 to 2.065 THz.

4GREAT
4GREAT consists of four co-aligned (to within a few arcsec) pixels at four different frequencies. The tuning ranges of these pixels are: 491-635 GHz (4G1), 890-1092 GHz (4G2), 1240-1525 GHz (4G3), and 2490-2590 GHz (4G4).

The GREAT instrument uses eXtended bandwidth Fast Fourier Transform Spectrometers (XFFTS) as backends. Each XFFTS has a bandwidth of 4 GHz and 16,384 channels, thus providing a resolution of 244 kHz (note that the useful bandwidth depends on the tuning and the atmospheric transmission). The beam size is close to the diffraction limit—about 14 x (1.9/ ν THz) arcsec, where ν is the frequency observed in THz.

A detailed description of the GREAT instrument and its performance during the 2011 Basic Science flights can be found in the GREAT special issue of Astronomy & Astrophysics (Heyminck et al. 2012, A&A, 542, L1). The upGREAT arrays are described in Risacher et al. (2016, A&A, 595, A34) and Risacher et al. (2018, JAI 7, 1849914). 4GREAT is described in Duran et al. (arXiv:2012.05106). Additional information about the instrument can be found on the GREAT website.

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6.1.1.1 Design

Heterodyne receivers work by mixing the signal from a source on the sky at a given frequency νs with the signal from a local oscillator (LO) at a specified (and precisely controlled) frequency νLO. This signal mixing results in two frequency bands on the sky called the signal and image bands being folded into the intermediate frequency (IF) band in the few GHz range, which is amplified and then spectrally analyzed. These bands are located symmetrically on either side of the LO frequency νLO, and they are separated from that LO frequency by an intermediate frequency νIF = |ν– νLO|. GREAT operates in a double sideband mode (DSB), which means that both the image and signal bands are not separated and are equally sensitive to incoming radiation. By definition, the band containing the spectral line of interest is always the signal band and the opposite band is the image band. This signal band can be chosen to be either above (Upper Sideband, USB) or below (Lower Sideband, LSB) the LO frequency; see Figure 6-1. For sources rich in spectral lines, care has to be taken so that a spectral line in the image band does not overlap or blend with the line of interest in the signal band. This can be achieved by fine-tuning the local oscillator frequency.

4G1 and 4G2 use Superconductor-Insulator-Superconductor (SIS) mixing devices providing an IF band from 4 to 8 GHz. 4G3 and 4G4 and the upGREAT arrays employ Hot-Electron-Bolometer (HEB) mixers with IF bands of 0.1 to 4 GHz. The optics of GREAT generally utilize beam splitters to overlay the LO and sky signal. However - due to LO power limitations - 4G4 uses a diplexer, which reduces the usable IF band to 1.4 to 2.8 GHz.

Figure 6-1.

Figure 6-1. Schematics of a GREAT receiver channel. Only 4G4 uses a diplexer, all other channels have a beam-splitter. The second IF mixing process is optional and is only used when the mixer output range and the backend input range do not match.

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6.1.1.2 Configurations

The channels that are currently operational are listed in Table 6-1. Not every frequency in each tuning range has been checked, so there may be gaps where the LOs do not provide enough power to pump the mixer or regions where the receiver temperature deviates from the average values quoted in the table.

Table 6-1

GREAT Configurations

Front-End

Frequencies (GHz)

Lines of Interest

DSB Receiver Temperatures (K)

Main beam efficiencies5

Beam Sizes5 (FWHP in arcsec)

Front-End

Frequencies (GHz)

Lines of Interest

DSB Receiver Temperatures (K)

Main beam efficiencies5

Beam Sizes5 (FWHP in arcsec)

HFA 1

4744.77749

[OI] 63 μm

1250

0.63

6.3

LFAH 2

1835–2007

[CII] 158 μm, CO, OH, 2Π1/2,
12CH, 13CH

1000

0.65

14.1

LFAV 2

1835–2007
2060–2065

Same as LFAH,
plus [OI] 145 μm

0.66

4G4

2490–2590

OH 2Π3/218OH 2Π3/2

3300

0.57

10.5

4G3

1240–1395
1427–1525

[NII] 205 μm, CO, OD, HCN,
SH, H2D+

1100

0.62

20

4G2 3,4

890–984
990–1092

CO, CS

> 600
300

0.55

27

4G1 4

491–555
560–635

NH3, [CI] 609 μm, CO, CH

< 150

0.61

52

  1. One 7-pixel array. Quantum Cascade Laser LO with very small tuning range near the [OI] 63 μm line.

  2. Two 7-pixel arrays at two polarizations (H,V). Both polarizations can be tuned to the same frequency (LFAH range), or two separate frequencies on a best effort basis. The [OI] 145 μm line is only tunable with the V-array LO.

  3. Strong degradation below 900 GHz.

  4. For 4G1 and 4G2, the gaps in the center of the LO tuning correspond to frequency ranges blocked by the low atmospheric transmission.

  5. From Duran et al. (arXiv:2012.05106)

In Cycle 10, GREAT offers two configurations:

upGREAT LFA with upGREAT HFA
This configuration employs the Low Frequency Array (LFA) in one dewar and the High Frequency Array (HFA) in the second dewar. The LFA consists of two polarizations (H and V) with 7 pixels each, and the HFA consists of 7 pixels. Both polarizations of the LFA array (LFAH and LFAV) can be tuned simultaneously in the 1.835-2.007 THz range (and specifically the [CII] line at 1900.536 GHz), or alternatively they can each be tuned to a different frequency on a best effort basis. The [OI]145 µm line can only be observed in V polarization. The pixels for both LFA polarizations are spatially co-aligned so tuning them both to the same frequency is equivalent to doubling the exposure time.

4GREAT with upGREAT HFA
This configuration implements 4GREAT in one dewar and the HFA in the second dewar. The 4GREAT pixels are coaligned on the sky to within a few arcseconds, and operate simultaneously.

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6.2 Planning Observations

 

This section describes the GREAT instrument and the available observing modes. It also contains additional information to estimate observing times in individual modes. 

If the frequency of interest is not listed in Table 6-1, please contact the GREAT team to ensure the feasibility of the observations. There may be gaps where the broadband Local Oscillators do not provide enough power to pump the mixers.

Note: Allan variance affects the capabilities of GREAT and requires special attention when planning observations, see Section 6.2.4 for details.

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6.2.1 Coordinates and Array Geometry

Because upGREAT maps can be rotated relative to standard sky coordinates (e.g., J2000), they have their own coordinate system defined as x and y. With a map rotation of 0 degrees, the +x axis is aligned with the +RA axis, and the +y axis is aligned with the +Dec axis (Fig. 6-2). The map rotation angle increases in the counter-clockwise direction, and this parameter can be set anywhere between -360° to +360°. For maps, scans in the x-direction are parallel to the x-axis, and scans in the y-direction are parallel to the y-axis.

Figure 6-2.

Figure 6-2. Left, The x/y map coordinate system is aligned with RA/Dec (J2000) for a map angle of 0°. Right, The x/y coordinate system at a map angle of +30°. The angle is measured in the counter-clockwise direction.

 

The upGREAT Low Frequency Array (LFA) and High Frequency Array (HFA) are arranged in a hexagonal pattern with a central beam. The spacings between the beams are approximately 2 beam widths (31.7 arcsec for the LFA, 13.8 arcsec for the HFA). For efficient mapping, the array is typically rotated by 19.1 degrees relative to the scan direction, resulting in a projected pixel spacing of 10.4 arcsec for the LFA and 4.6 arecsec for the HFA (see Fig. 6-3). The array can be rotated independently of scanning direction for maximum flexibility during observation planning.

Figure 6-3.

Figure 6-3. Left, The configuration of an upGREAT array. The numbers 0-6 mark the pixel numbers of the array, and the separation between the pixels, r, is 31.7 arcsec for the LFA, and 13.8 arcsec for the HFA. Right, An upGREAT array, rotated by -19.1° (pixel 1 is labeled) with arrows indicating the scan direction. The projected pixel spacing perpendicular to the scan direction is 10.4 arcsec for the LFA, and 4.6 arcsec for the HFA.

When creating a mapping strategy, observers will have to weigh many factors such as the area to be mapped, the required integration time per point, and of course the scientific objectives. Examples given in Section 6.2.3.3 aim to provide guidelines

Figure 6-4. 

Figure 6-4. Comparison of the footprints for each GREAT array. From top to bottom: 4G4, 4G1, LFA, and HFA. This example shows an on-sky visualization of each array using USPOT and Single Point AOTs in Dual Beam Switching mode. The red stars identify the central position for each array, and the blue circles represent their on-source footprints. The green and magenta circles respectively show the two reference positions.

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6.2.2 Observing Modes Overview

Two observing modes are currently offered: Total Power (TP) and Beam Switching (BSW), the latter of which is available as either Single Beam Switching (SBS) or Dual Beam Switching (DBS).

Total Power Mode
In Total Power mode, the telescope alternates between the target and a nearby reference position that is free of emission. The GREAT software then produces a spectrum from the difference between measurements on the target (ON) and reference (OFF) positions. The optimal integration time in this mode depends on the stability of the receiver and the rate of atmospheric fluctuations. Typically, the recommended integration times on the ON position are: < 20 s for the HFA, < 30 s for the LFA, and < 50 s for 4GREAT. Shorter integration times provide a better cancellation of atmospheric fluctuations, but at the cost of a reduced observing efficiency due to overheads. The ON-OFF cycle is repeated until the required sensitivity is reached. 

Total Power mode is most often used to maximize the observing efficiency of On The Fly maps, as well as for single point observations in crowded regions with significant extended emission. Reference positions that are far from the target position may result in poor baselines due to temporal fluctuations in the sky background. If a reference position cannot be identified within 30 arcmin of the target, an intermediate reference position can be selected instead even if it potentially has some emission from the line of interest. This intermediate position will then be measured against a faraway reference position with no line emission. Any contamination in the original spectrum due to line emission in the intermediate reference position can then be accounted for and removed.

Beam Switching Mode (BSW)
In Single Beam Switching (SBS) mode, the telescope is pointed at an intermediary position between the target and reference positions while the secondary mirror is chopped. The main parameters for this mode are the chop throw, which is the angular distance between the target and reference position, and the chop angle relative to the chosen reference frame (i.e., sky coordinates or telescope assembly). 

In Dual Beam Switching (DBS) mode, there are instead two reference positions placed symmetrically around the target position. In addition to chopping the secondary mirror like for the SBS mode, the telescope nods between two intermediary positions so that the target is measured against each reference position alternatively.

While using either beam switching modes, the secondary mirror typically chops at a rate between 0.6 and 1.3 Hz. The maximum chop throw allowed is 5 arcmin due to the physical limitations of the secondary mirror. Because the time between the ON and OFF Positions is short (~1 s), this the beam switching modes typically results in better sky cancellation and better baseline stability than Total Power.

Beam switching modes are most often used for point or compact sources for which there is a nearby reference position clear of emission. Smaller chop throws between 60 and 180 arcsec are usually preferred to limit pointing errors and beam distortions (coma). In most cases, DBS mode is preferred over SBS mode, since it results in a better baseline stability.

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6.2.3 Astronomical Observation Templates (AOTs)

GREAT offers five standard Astronomical Observation Templates (AOTs) in USPOT: Single Point, Raster Mapping, On The Fly (OTF) Mapping, OTF Array Mapping, and OTF Honeycomb Mapping. Each AOT can  be run in either Total Power or Beam Switching modes.

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6.2.3.1 Single Point

The Single Point AOT is used to observe a single position on sky. It is typically used to observe faint sources that require long integration times.

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6.2.3.2 Raster

Raster mapping is essentially a collection of single point observations used to create small maps where a relatively long integration time per map point is needed.

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6.2.3.3 On the Fly (OTF)


In an OTF map, the telescope scans along a series of rows while the back-ends are continuously integrating the incoming signal. An average is recorded after the telescope has moved a specific distance on the sky. Typically, the size of these steps is half of the beam width. Using default mapping parameters, each point in the central region of an OTF map will be covered at least once by each pixel of the array (either the HFA or the LFA). The size of this central region changes as a function of the mapping parameters, and it can be assessed easily with USPOT's visualization options (see the examples in Section 6.2.3.3).

The three (OTF) mapping options are OTF mapping (also referred to as Classic OTF), OTF Array mapping, and OTF Honeycomb mapping. Each OTF Astronomical Observation Template (AOT) can be used with the two instrument configuration of GREAT: LFA H/V and HFA, and 4GREAT and HFA. However, please keep in mind that OTF Array and OTF Honeycomb maps are not designed to be used with the single pixel of 4GREAT. Otherwise, the parameters for OTF observing schemes are flexible and can be easily modified in USPOT depending on the needs of the project. The recommended parameters presented in this section should perform well for most mapping projects. 

Any OTF AOT can be executed in Beam Switching (BSW) or Total Power (TP) mode.

In Total Power mode, each row scan is preceded by a measurement of the reference position. The integration time tOFF on this reference position before each scan is tOFF = NON0.5 x tON, where NON is the number of steps in the row and tON is the on-source exposure time per point. In this mode, the size of a scan row is limited by the stability of the receiver and by atmospheric fluctuations. The recommended time to complete a single row is under 20s for the HFA, under 30s for the LFA and under 50s for 4GREAT. In addition, the typical on-source exposure times per point are between 0.3 s and 2.0 s. Large maps (> 10 arcmin for the LFA and > 3 arcmin for the HFA) should therefore be divided into smaller sub-maps to ensure receiver stability during observations. 

In Beam Switching mode, the secondary mirror chops while the telescope is scanning along each row. No dedicated reference position is needed, and so the telescope can immediately start the next row. However, the times spent integrating on the source and reference positions are equal, and so the observing efficiency of the Beam Switching mode is still lower than for the Total Power mode. This mode is rarely used for OTF maps, but it can nonetheless be useful for small maps of compact regions where a stable baseline is needed for the detection of the line observed

Some things to consider when deciding between these two modes are:

Efficiency
Maps obtained using BSW modes need an equal amount of integration time on the ON and OFF positions. In contrast, Total Power maps spend less time on the OFF position, and are therefore more efficient.

Baseline Stability
BSW observations generally have better baseline stability. If the source is expected to have faint and/or wide lines, then BSW modes should be preferred. If the source is expected to have bright and/or narrow lines, then the baseline quality is less of an issue.

Reference positions
For a BSW map, there needs to be an emission-free region on the sky that is the same size as the OTF map and within a few arminutes of the map. Finding such a reference position is often a challenge, especially in crowded regions or region with significant extended emission. For Total Power maps, only a single emission-free pointing is needed as a reference position, and it can be significantly farther away from the source (up to 30 arcmin, although baselines will be better for closer reference positions).

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6.2.3.3.1 Classical OTF Mapping

The classic OTF mapping can be used effectively with any of the GREAT arrays. For an OTF mapping, each array pixel creates a fully-sampled rectangular map based on the step size along the scan row and the spacing between each row. For the upGREAT arrays (LFA and HFA), the result is seven overlapping rectangular maps (see Section 6.2.3.3.1a and Section 6.2.3.3.1b). Classic OTF mapping is currently the only available OTF AOT that can create fully-sampled maps using the single-pixel 4GREAT array.

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6.2.3.3.1a LFA OTF Mapping example

In this example, we design an OTF map in Total Power mode to measure [CII] 158 µm line emission in NGC 1333 using the LFA as the primary array. The final map is composed of 14 fully-sampled maps of the central region combining both the LFAH and LFAV polarizations. The step size in the x-direction and the y-direction are set to 6 arcsec. Both the number of steps per row and the number of rows are both set to 60, which provides a 360 arcsec-wide square map (see Fig. 6-5). The array rotation is set to -19.1 degrees.

The on-source exposure time per point is 0.5 s, and so each row scan is completed in 30 s. The time spent on the off-position before each scan is therefore 3.9 s, and so the on+off time for each scan is 33.9 s. For 60 rows, the total integration time for the map is 33.9 minutes, and the total observing time including overheads is approximately 67.8 minutes. For a single coverage of the map, two polarizations, and seven pixels, the effective integration time per point for the central region will be Ton = 1 x 2 x 7 x 0.5 s = 7 s. Using the GREAT time estimator in SITE, we find a RMS temperature ΔTA* of 0.42 K assuming a resolution of 1 km/s, a line width of 10 km/s, an altitude of 41,000 ft, and an elevation of 40 degree. 

Figure 6-5.

Figure 6-5. Overlay of an OTF map designed for the LFA+HFA configuration. The primary array is the LFA. Each red rectangle shows the region mapped by one of the LFA pixels. The footprint of the array is shown by the red circles and marks the starting position of the map. The central region of the map is covered once by each pixel of the array. In this configuration, the HFA will produce a significantly under-sampled map due to the large step size (6 arcsec). 

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6.2.3.3.1b 4GREAT and HFA OTF mapping example

In this example, we design an OTF map in Total Power mode of the same region as previously. This time we plan to measure the [OI] 63 µm line with the HFA and the 12CO J=22-21 line with 4G4. All 4GREAT receivers observe simultaneously, but we choose 4G4 for this example because it has the closest beam size (9.9 arcsec) to the HFA (5.2 arcsec). The final results will be 7 fully-sampled [OI] maps of the central region with the HFA and one over-sampled CO map with 4G4. The step size in the x-direction and the y-direction are set to 3 arcsec. Both the number of steps per row and the number of rows are both set to 60, which provides a 180 arcsec-wide square map (see Fig. 6-6). The array rotation is set to -19.1 degrees.

The on-source exposure time per point is 0.3 s, and so each row scan is completed in 18 s. The time spent on the off-position before each scan is therefore 2.3 s, and so the on+off time for each scan is 20.3 s. For 60 rows, the total integration time for the map is 20.3 minutes, and the total observing time including overheads is approximately 40.6 minutes. For a single coverage of the map, one polarization, and seven pixels or one pixel, respectively, the effective integration time per point for the central region will be Ton = 1 x 1 x 7 x 0.3 s = 2.1 s for the HFA and Ton = 1 x 1 x 1 x 0.3 s for 4G4. Using the GREAT time estimator in SITE with a resolution of 1 km/s, a line width of 10 km/s, an altitude of 41,000 ft, and an elevation of 40 degree, we find a RMS temperature ΔTA* = 0.88 K for [OI] 63 µm and ΔTA* = 5.3 K for 12CO J=22-21. 

Figure 6-6.

Figure 6-6. Overlay of an OTF map designed for the 4G+HFA configuration. The primary array is the HFA. Each red rectangle shows the region mapped by one of the HFA pixels. The footprint of the array is shown by the red circles and marks the starting position of the map. The central region of the map is covered once by each pixel of the HFA, as well as by the single pixel of 4GREAT. In this configuration, the resulting 4GREAT maps will be significantly over-sampled due to the small step size (3 arcsec). USPOT can only show the HFA visualization when using the 4G+HFA instrument configuration.

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6.2.3.3.2 OTF Array Mapping

An OTF Array map is created in a similar fashion to a classical OTF map; the telescope scans along a series of rows while the back-ends are continuously integrating the incoming signal. The main difference is that the distance between scan rows is not constant, and is instead designed so that each map point is covered by a single pixel of the array (assuming default mapping parameters). OTF Array maps are typically a combination of several scan "blocks", and are often used to observe relatively compact regions expected to have bright line emission.

The basic unit of the upGREAT array mapping scheme is referred to as a block, which consists of a single or multiple scans of the same length, in the same direction (Fig. 6-7). For both the LFA and the HFA, the projected pixel spacing (after rotating the array by -19.1 degrees) is such that a single scan results in an under-sampled map. To create a fully sampled map, it is necessary to make at least one more scan to fill in the gaps between pixels. The default behavior is to make a second scan, creating a fully sampled map and completing the block. It is possible, however, to scan only a single time (creating an under-sampled map), or more than two times (creating an over-sampled map), depending on the goals of the project. 

Figure 6-7.

Figure 6-7. Left, A block that consists of a single scan of the rotated array. The gaps between the scans indicate an under-sampled map. Right, A block that consists of two scans. This block is fully sampled in the direction perpendicular to the scan direction. The second scan fills in the gaps in the single-scan block.

A single map can consist of any number of blocks, and can scan in the x- or y- direction, or both. The parameters of the x- and y-direction scans are independent, but can be used in concert to create fully-sampled maps of a region in both directions (Fig. 6-8). Scanning in both directions helps to minimize striping effects that can be caused by the different characteristics of individual array pixels.

Figure 6-8.

Fig. 6-8. Left: A map composed of six blocks scanning in the x-direction. There are three blocks along the scan direction, and two blocks perpendicular to the scan direction. The region within the two vertical white lines shows the inner coverage region. Right: A map composed of six blocks scanning in the y-direction. There are two blocks along the scan direction, and three blocks perpendicular to the scan direction. The region within the two horizontal white lines shows the inner coverage region. Maps scanning in both directions can be set up so that the central regions of each map align.

To calculate the size of the inner coverage region along the scan direction:

inner coverage = [(block length) * (# of blocks in scan direction) – 1] * (array size)

where block length is in units of the array size.

To calculate size of the inner coverage region perpendicular to the scan direction:

inner coverage = (# of blocks perpendicular to scan direction) * (array size)

Because of the flexibility of this mapping scheme, there can be multiple ways to observe the same region. For example, the two setups in Fig. 6-9 fully cover the same area. Some important factors to consider to differentiate thse options are the desired integration time per point, the step size, and the duration of a single scan.

Figure 6-9.

Figure 6-9. Left: A map consisting of two blocks, each one 2*(array width) long. Right: A map consisting of a single block that is 4*(array width)-long. The total inner coverage for both maps is the same.

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6.2.3.3.2a LFA OTF Array mapping example

In this example, we design an OTF Array map in Total Power mode to measure [CII] 158 µm line emission in NGC 1333 using the LFA as the primary array. The final map is composed of 2 horizontal and 2 vertical blocks to cover the region of interest (see Fig. 6-10), which are covered by both polarization of the LFA. The parameters in USPOT for this setup are 1 block in the scan direction and 2 blocks perpendicular to the scan direction for both the x and y scans. Each block is set to a width of 3 arrays, which leads to 42 points on each scan with the default step size for the LFA of 5.2”. The array is automatically rotated by -19.1 degrees. The number of lines per block is 2 optimally sampling map. 

The on-source exposure time per point is 0.5 s, and so each row scan is completed in 21 s. The time spent on the off-position before each scan is therefore 3.2 s, and so the on+off time for each scan is 24.2 s. For each block of two rows, the total integration time for the map is 48.4 s, and the total observing time including overheads is approximately 96.8 s. The total observing time for all four blocks is therefore 6.5 minutes. For a single cycle of the OTF Array map, each position in the central region of the map is going to be covered once in each scan of the two scan direction. With both polarizations, the effective integration time per point for the central region will therefore be Ton = 1 x 2 x 2 x 0.5 s = 2 s. Using the GREAT time estimator in SITE, we therefore find a RMS temperature ΔTA* of 0.8 K assuming a resolution of 1 km/s, a line width of 10 km/s, an altitude of 41,000 ft, and an elevation of 40 degree. 

Figure 6-10.

Figure 6-10. Overlay of an OTF Array map in the LFA+HFA configuration. The primary array is the LFA. Each red rectangle shows one of the array blocks described in Section 6.2.3.3.2. In this configuration, the HFA will produce a significantly under-sampled and inhomogeneous map due to the large step sizes and tiling based on the LFA array size. 

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6.2.3.3.3 OTF Honeycomb Mapping

An OTF Honeycomb map is the preferred solution for compact objects that are comparable in size to the array used (either the LFA or HFA). Instead of scanning rows, the telescopes follows a small 25-points hexagonal pattern in order to fully-sample the gaps between each array pixel on the sky. The resulting map is fully-sampled at the resolution of the respective array. This avoids the issue of wasted integration time outside the region of interest, depending on the size and geometry of the target, by avoiding not fully covered edges common to the classical OTF and OTF Array modes.

Like OTF Array maps, OTF Honeycomb maps can be tiled together to map larger regions. However, OTF and OTF Array maps are recommended for regions larger than a few times the array size in order to obtain a more homogeneous noise map by covering each map point with different array pixels.

In this OTF mode, the telescope moves while integrating not in a straight line, but instead by spiraling in a 25-point hexagon pattern filling in the space between the pixels of the array. Figure 6-11 shows this pattern for all pixels, thus illustrating how all pixels combined completely fill the mapping area.

Figure 6-11.

Figure 6-11. Honeycomb pattern for the LFA with all pixels showing how the pointings mesh together. The units of the axes are in arcseconds. The patter for the HFA will be a factor of 2.7 smaller since the pattern scales with the array size.

When executing an OTF honeycomb map with the HFA in tha LFA+HFA configuration, the LFA will produce 7 small oversampled maps centered around each LFA pixel locations, with gaps between each of these small maps. Alternatively, when executing an OTF honeycomb map with the LFA, the HFA will produce a sparse map the size of the LFA mapping area.

When planning an OTF honeycomb map, one needs to select the Time Per Point so that one OTF scan, the 25-point pattern, does not take longer than 20 or 30 seconds, for an HFA or LFA map respectively. Each location in the mapping area will be covered only once by one pixel (two for the LFA, if both polarization of the LFA are tuned to the same frequency). Repeat the 25-point pattern (the cycle parameter in USPOT) as often as necessary to reach the integration time per map position estimated with SITE.

The OTF honeycomb pattern can also be tiled, though ideally do not tile more than a few tiles at once; larger maps are covered more efficiently when using the other OTF modes. Each honeycomb tile requires its own AOR, and tiling can be done by offsetting the next tile from the first by moving the AOR center by the following vector (±2.5, ±0.866). The unit of this separation vector is in array sizes, and the angular size is obtained by multiplying it with 31.7 arcsec for the LFA, and 13.8 arcsec for the HFA. Rotate the vector by 60 degrees for adjacent tile positions and/or extend the map in the same way from a new AOR center. Below is an illustration of such a tiling with eight tiles. In practice, please consider the other OTF maps modes for such a large mapping area.

Figure 6-12.

Figure 6-12. How a honeycomb map is tiled: Each symbol is a different pixel, each color is a different tile. The snowflake-shaped outline is how each AOR is visualized in USPOT. The left and bottom axes show the size of the tiling for the LFA, and the right and top axes show the size of the tiling for the HFA. The offset of each honeycomb tile is given in Table 6-2.

Table 6-2 

Example of Honeycomb Tiling Offsets

 

LFA

HFA

 

LFA

HFA

Tile 0

(0”,0")

(0”,0")

Tile 1

(-79.25”,+27.45")

(-34.50”,+11.95")

Tile 2

(-15.85”,+82.36”)

(- 6.90”,+35.85”)

Tile 3

(+63.40”,+54.91”)

(+27.60”,+23.90”)

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6.2.3.3.3a LFA OTF Honeycomb mapping example

In this example, we design an OTF Honeycomb map in Total Power mode to measure [CII] 158 µm line emission in NGC 1333 using the LFA as the primary array. The final map is composed of the 4 individual tiles defined in Fig. 6-13 to cover the region of interest (see Fig. 6-13), which are covered by both polarization of the LFA. The parameters in USPOT for each tile are a pattern angle of 0.0 degrees and the Target Offset RA and Target Offset Dec values defined in Table 6-2 for the LFA. 

The on-source exposure time per point is 1.0 s, and so each tile is completed in 25 s. The time spent on the off-position before each scan is therefore 5.0 s, and so the on+off time for each scan is 30.0 s. The total observing time including overheads is approximately 120 s. The total observing time for all four tiles is therefore 8 minutes. For a single cycle of the OTF Honeycomb map, each position in the central region of the map is going to be covered once during the scan, but with two polaritzations. The effective integration time per point for the central region will therefore be Ton = 1 x 1 x 2 x 1.0 s = 2 s. Using the GREAT time estimator in SITE, and using the Total Power OTF option with a Non of 25, we find a RMS temperature ΔTA* of 0.8 K assuming a resolution of 1 km/s, a line width of 10 km/s, an altitude of 41,000 ft, and an elevation of 40 degree. 

Figure 6-13.

Figure 6-13. Overlay of 4 OTF Honeycomb tiles in the LFA+HFA configuration. The primary array is the LFA. Each "hexagon" one of the tiles described in Section 6.2.3.3.3. The yellow circles represent the corners of the pattern drawn by the central pixel of the LFA. In this configuration, the HFA will produce an under-sampled and inhomogeneous map due to the large step sizes and tiling based on the LFA array size. 

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6.2.4 Spectroscopic Stability Limitations

As mentioned in Section 6.2, the spectroscopic stability (e.g., Allan variance) sets limits to the operation of a heterodyne instrument like GREAT.

Beam Switching modes typically operate with a chop frequency around a few tenths of a Hz to a few Hz, which is relatively fast, and so the observing limitations are mainly set by the atmospheric stability. As such, on-source integration times of 50s for 4GREAT, 30 s for the LFA, and 20 s for the HFA are typically implemented to achieve optimal spectroscopic stability. A Dual Beam Switching mode is recommended, when possible, in particular for projects aiming to measure weak and/or broad lines. Some performance decrease has been observed when using a Single Beam Switching mode instead, but it is a viable alternative for crowded regions.

For a Total Power mode, the situation is more complicated and multi-dimensional. Observing line widths larger than a few hundreds MHz and using a reference position farther than 30 arcmin from the source position may negatively impact the stability of the spectroscopic baseline. These impacts depend on the frequency observed, the weather conditions, the stability of the sky background, the elevation of the source, and the arrays used. Please contact the SOFIA help desk if your Total Power observations require a faraway reference position and/or if the line of interest is expected to be weak and broad.

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6.2.5 Estimation of Exposure Times

Estimations of exposure times for GREAT can be made using the SOFIA Instrument Time Estimator (SITE). SITE is a web-based tool that calculates either the signal-to-noise ratio for a given line brightness and integration time, or the integration time needed to reach a certain RMS noise level for either one point on the sky or per map position for an OTF map in Total Power mode. These integration times do not include tuning, chopping, slewing, and other observatory overheads. The total time, including all overheads, is determined in USPOT after entering the time calculated by SITESITE is also useful to determine which sideband is the best to use as the signal band by taking the atmospheric transmission into account. System temperatures for the line in the USB or LSB are given, as well as a plot showing the line locations for either Local Oscillator tuning compared to the atmospheric transmission.

The time estimator calculates the rms noise temperature reached after a given integration time, or it calculates the time needed to reach a given SNR for a given peak brightness temperature by calculating the system temperature and solving the standard radiometric formation for a single point observation. See Section 6.3 for more details on calculations and temperature scale used.

Note that currently, SITE works on the TR* temperature scale. It will be switched to work on the TA* temperature scale. The temperature scales are relate as follows TA* = ηfss TR* with ηfss = 0.97. The 3% difference in the two temperature scales has no practical effect on the time estimate.

GREAT is a dual sideband receiver, which means that it simultaneously observes in two frequency bands: the upper sideband (USB) and the lower sideband (LSB). The transmission plot in SITE shows the locations of each sideband relative to the observed line, depending on which sideband is used as the signal band. The sidebands for the LFA, HFA, 4G3, and 4G4 are separated by +/- 1.5 GHz, while for 4G1 and 4G2 they are separated by +/- 5.5 GHz for 4GREAT bands 1 and 2. The required integration times are calculated for both sidebands. The lowest value provided by SITE should be typically used for the time estimate in a proposal. Differences in the calculated integration times for the LSB and USB are due to the frequency dependence of the atmospheric transmission.  

Description of SITE Input Parameters

Type of Observation
Select "Single Point or Beam Switch OTF/Raster Map" for single point observations in either total power or beam-switched mode, and for OTF/Raster maps observations in beam-switched mode. Select "TP OTF/Raster Map" for OTF/Raster maps in total power mode.

Rest Frequency
Enter the rest frequency (in THz, using 7 decimal places) of the line you wish to observe. The current tuning ranges for the GREAT receivers are listed in Table 6-1.

Frequency or Velocity Resolution
Enter the frequency (in MHz; select the "MHz" radio button) or velocity (in km/s; select the "km/s" radio button) resolution that is requested in the final spectrum.

Line Width
Enter the frequency (in MHz; select the "MHz" radio button) or velocity (in km/s; select the "km/s" radio button) window that will be used to calculate the atmospheric transmission. Modifying this parameter may be important if the line you wish to observe falls close to a narrow atmospheric feature.

Total Power Map Parameters
For OTF maps: Enter the number of ON positions (steps or dumps) in each OTF scan row in the Non field, or have the time estimator calculate this value for you. If you choose to have the estimator calculate it, you should enter the dimensions of the map (in arcsec) and select a "Map Type" option (Classical OTF or Array OTF). For a Classical OTF map, the "Map Size" refers to the area mapped by the central pixel only. For an Array OTF map, the "Map Size" refers to the area that will be fully-sampled (i.e., the array width is added to the length of each scan). The Array OTF map should only be selected if the frequency falls within the tuning range of the LFA or HFA (see table above).

Using these inputs, the calculator evaluates scanning in both x- and y-directions, and selects the direction that has fewer scan lines. It then estimates Non using the length of the scans and a frequency-based receiver stability time. The step sizes assumed for each frequency band are: 3 arcsec for the HFA, 6 arcsec for the LFA, 25 arcsec for 4G1, 12 arcsec for 4G2, 8 arcsec for 4G3, and 5 arcsec for 4G4. Note that there are many ways to configure a mapping observation, and the calculated value of Non is only one of many possible values. For an OTF Honeycomb, Non should be set to 25. 

For Raster maps: Enter the number of on positions that will be used for each reference position in the Non field. You may ignore the Map Size and Map Type fields.

Signal to Noise Ratio / Integration Time
If the SNR radio button is selected, enter the desired signal to noise ratio in this field and the estimated line strength in the Brightness Temperature field. The time estimator will calculate the integration time required to reach this SNR. If the Integration Time radio button is selected, enter the integration time (in seconds) for your observation. If your observation is a Total Power OTF map or a Total Power raster map, enter the effective on-source exposure time per map point. Otherwise, enter the ON+OFF integration time. The time estimator will calculate the 1-sigma rms sensitivity (in units of TR*) based on the input integration time.

Brightness Temperature TR* (K)
Enter the estimate of the peak brightness temperature of your line. This field is only used if the SNR radio button is selected (see above). As is the case for other heterodyne receivers that use hot and cold loads to measure the receiver temperature, the intensity units are Kelvin (K). The intensity scale used in the online tool is the brightness temperature TR*. This relates to the measured antenna temperature as TR* = TA* / ηfss with ηfss = 0.97. The main beam temperature (corrected for losses in the side lobes) as TMB = TA* / ηmb . The main beam efficiencies have been measured from planetary observations, and are listed in Table 6-1. A detailed description of the temperature scales, unit conversion, and how SITE calculates noise temperatures is given in Section 6.3.

Source Velocity
Enter the source velocity (in km/s) in the Local Standard of Rest (LSR) reference frame.

Observer Velocity
Enter the velocity of the observatory with respect to the LSR on the date of the observation. If this is unknown, you may either leave the default (0 km/s) or enter the date, time, coordinates, and location for your observation to have the time estimator calculate the observer velocity automatically. Note that if your desired line rest frequency falls close to or in an atmospheric absorption feature, you may still be able to observe the line if you choose the right time of the year as the source is blue- or red-shifted relative to the atmospheric feature.

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6.2.6 The GREAT Exposure Mapper Program

The GREAT Exposure Mapper Program can generate two-dimensional maps of the instrument exposure time, sensitivity (noise level), simulated data, and signal-to-noise.  It can be installed on a local machine, or run online.  By uploading a .aor file from DCS or USPOT, you can visualize GREAT maps and test different mapping strategies.

Figure 6-14.

Figure 6-14. Example 2D sensitivity plot generated by the GREAT Exposure Mapper Program for an LFA Honeycomb OTF map tuned to the [CII] line and binned to 1 km/s spectrally and 6”x6” pixels spatially.

For the latest version of the GREAT Exposure Mapper Program, link to the online notebook, and instructions on how to install and run, please visit:

https://github.com/kfkaplan/the_greatest_sensitivity_mapper

Note that the GREAT Exposure Mapper Program is still under development and not yet fully supported.  It is provided to the community as a best effort for Cycle 10.  It is highly reccomended that you check the results against SITE or your own calculations.  Please direct all questions, comments, and bug reports to Kyle Kaplan (kkaplan@usra.edu).

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6.3 Details on GREAT Sensitivities

6.3.1 Temperature Scales

The GREAT integration times are calculated with the SOFIA Instrument Time Estimator (SITE). It will use the temperature scale.

Note that currently, SITE works on the TR* temperature scale. It will be switched to work on the TA* temperature scale. The temperature scales are relate as follows TA* = ηfss TR* with ηfss = 0.97. The 3% difference between the two temperature scales has no practical effect on the time estimate.

Typical for radio astronomy (The notations and formulas mostly follow the book “Tools of Radio Astronomy” by Wilson et al. also taking inspiration from Kutner and Ulich (1981) and Downes (1989)), GREAT works with brightness or radiation temperatures in Kelvin defined by the Rayleigh-Jeans law.

(Eq. 6-1)

with the wavelength, the frequency, the speed of light, the Stefan-Boltzmann constant, and the specific intensity or brightness.

The antenna temperature is defined by equaling the power output of a resistor at temperature due to thermal noise to the power received by an antenna. The power per unit bandwidth is

(Eq. 6-2)

The power received in one polarization from a source with an brightness distribution subtending the solid angle on the sky, by an ideal antenna outside of the atmosphere with the normalized antenna patternwith an effective apertureis

(Eq. 6-3)

By convention, the antenna temperature of such an ideal antenna is denoted with and combining the above equations we get:

(Eq. 6-4)

Using the étendue or throughput of the antenna with the antenna’s solid angle , one can re-write the expression as:

(Eq. 6-5)

To get from the measurement of with a real antenna through atmosphere to the ideal additional factors need to be accounted for, leading to the different temperature scales used in radio astronomy.

  • Antenna temperature Actual measured noise temperature of antenna including inefficiencies and all other noise sources including the atmosphere. Guan et al. (2012, A&A 542, L4) discusses the calibration scheme for GREAT, i.e. how to get from to .

  • Forward beam brightness temperature The convolution of the source brightness with the full forward antenna response. Also known as corrected antenna temperature, because it is the observed source antenna temperature corrected for atmospheric attenuation, radiative loss, and rearward scattering and spillover.

  • Main-beam brightness temperature The convolution of the source brightness distribution on the sky with the main-beam profile of the telescope.

These temperature scales are related in the following way

(Eq. 6-6)

with

(Eq. 6-7)

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6.3.2 Conversion from Temperature to Flux Density

For many reasons, one might want to convert the brightness temperatures to spectral flux densitiesin e.g. Jansky. Let be the spectral flux density of a source in the beam. Then the relation between and or is according to Eq. 6-4 and the throughput

(Eq. 6-8)

Plugging in numbers from Table 6-1 for the LFAV (, FWHP) we get sr (assuming a Gaussian beam) and using =157.741µm (wavelength for [CII]), the conversion factors become

(Eq. 6-9)

Note that these conversion factors do not depend on the wavelength.
They vary only slightly for the receivers due to varying efficiencies.

When dealing with integrated line fluxes, one may need to convert between e.g. K km/s and W/m2. The same conversion as above applies, one just needs to additionally convert the in km/s to a in Hz. For a [CII] line that means

(Eq. 6-10)

Note that this conversion factor does depend on the wavelength.

The table below gives the conversion factor for the receivers at a typical frequency for each receiver.

 

HFA

LFAV

LFAH

G4

G3

G2

G1

 

HFA

LFAV

LFAH

G4

G3

G2

G1

(Jy/K)

1140

890

904

1130

944

1170

1020

(Jy/K)

731

588

588

645

585

643

621

(units as above)

1.16

0.372

0.372

0.576

0.261

0.233

0.110

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6.3.3 Details on the Integration Time Estimate

This section presents the background of the integration time calculations in SOFIA Instrument Time Estimator (SITE).

In a first step, the system temperaturegets calculated. Three main contributions are considered in SITE. The receiver temperature varies over the bandpass which is determined in lab measurements (see Guan et al., 2012, A&A 542, L4). It varies over the bandpass depending on the intermediate frequency (IF). SITE assumes an optimal value for, because the frequency to be observed will be placed optimally in the bandpass. However, one needs to realize that the noise increases significantly towards the edges of the 4GHz wide bandpass. Contact the helpdesk, if a spectrum wider than ∼1GHz is needed. Other noise sources are the emission from the skyand the telescope. These noise sources add up as

(Eq. 6-11)

The factor 2 account for the noise entering from both side bands (assumed to be equal). The factors and account for losses by absorption by the sky and the telescope, respectively. The efficiencies in the denominator correct the noise temperatures from thescale to thescale.

Here is a detailed example how the value ofgiven by SITE for the [CII] line at 1.9THz is calculated. The temperaturesandare radiation temperatures. Assuming blackbody radiation of a temperaturethe radiation temperatureis

(Eq. 6-12)

Since the efficiencies are transmission factors,are absorption factors, which are equal to emissivities. Thus, with the respective efficiencies and radiation temperatures. For a physical temperature of 188K for the telescope assembly and a telescope efficiency of = 0.92, we find at 1.9THz

(Eq. 6-13)

Assuming an air temperature of 178K and an atmospheric transmission =0.86, we find at 1.9THz

(Eq. 6-14)

With a receiver temperature =1000K, we get

(Eq. 6-15)

which is close to what SITE calculates not assuming that both sidebands contribute equally to the system noise as we did here.

In a second step, SITE uses the radiometer formula for a switching (aka chopping) radiometer to calculate the root-mean-square (rms) noise temperatureachieved after a total integration time (on- and off-chop integration time) for a spectral resolution of:

(Eq. 6-16)

Thus, aiming for a spectral resolution of =0.5km/s or =3.2MHz for a [CII] line, one can achieve=0.10K in 900 seconds of total integration time. This applies for all beam-switched aka chopped observations and single-point total-power observations.

For a total-power (TP) raster or on-the-fly (OTF) maps, the spectrum taken in the off-position is subtracted from on-positions. The optimal integration at the off-position is , where is the integration time per on-position. In contrast to above, the integration time is different in the on- and off-position. In this case, the rms-noise comes out as

(Eq. 6-17)

which becomes the same equation as above for .

Again, aiming for a spectral resolution of =0.5km/s or =3.2MHz for a [CII] line and withand , one can achieve=1.6K. SITE and this calculation takes only one pixel into account. See the examples in Sect. 6.2.3.3 for mapping with the array receivers.

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