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The German REceiver for Astronomy at Terahertz Frequencies (GREAT) is a dual channel heterodyne instrument that will provide high resolution spectra (up to R = 10^{8}) in several frequency windows in the 0.490–4.74477749 THz range.
The front-end unit consists of two independent dewars that operate simultaneously. Each dewar contains one of the following channels:
upGREAT Low Frequency Array (LFA)
The GREAT instrument uses Fast Fourier Transform (FFT) spectrometers as backends. Each XFFTS spectrometer has a bandwidth of 2.5 GHz and 64,000 channels, providing a resolution of 44 kHz. The beam size is close to the diffraction limit—about 14 arcsec at 160 μm.
A detailed description of the GREAT instrument and its performance during Basic Science can be found in the GREAT special issue (Heyminck et al. 2012, A&A, 542, L1). The LFA is described in Risacher et al. 2016 (A&A, 595, A34). Because the instrument is regularly being upgraded and its performance improved, always check the GREAT website for the latest information.
Heterodyne receivers work by mixing the signal from a source at a given frequency ν_{s} with that from a local oscillator (LO) at a specified (and precisely controlled) frequency ν_{LO} and amplifying the result. The mixing results in two frequency bands, called the signal and the image bands, located symmetrically on either side of ν_{LO} and separated from ν_{LO} by the intermediate frequency ν_{IF} = |ν_{s }– ν_{LO}|. GREAT operates in double sideband mode, i.e. both the image and signal bands are equally sensitive to incoming radiation. By definition the spectral line of interest is always placed in the signal band, which can be chosen to be either above (Upper Sideband, USB) or below the LO frequency (Lower Sideband, LSB); 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 in the signal band.
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.
Front-End | Frequencies (GHz) | Lines of Interest | DSB^{5} Receiver Temperatures (K) |
---|---|---|---|
upGREAT LFA | 1810–2070 | [OI], [CΙΙ], CO, OH^{2}π_{1/2} | 1000 |
upGREAT HFA | 4744.77749 | [OI] | 1100 |
4GREAT | 490–635^{1} | NH_{3}, [CI], CO, CH | 120 |
890–1100^{2} | CO, CS | 350 | |
1200–1500^{3} | [NII], CO, OD, HCN, SH, H_{2}D^{+} | 800 | |
2490–2590 | OH^{2}π_{3/2 }, ^{18}OH^{2}π_{3/2} | 1500 |
In Cycle 8, GREAT offers two configurations:
Each of the two installed mixers is provided with XFFTS Fast Fourier Transform spectrometers. The XFFTS has a 2.5 GHz bandwidth and 64,000 channels, providing a resolution of 44 kHz.
The usable instantaneous bandwidth is generally less than that covered by the XFFTS, generally about 1-1.5 GHz. The tuning range of the HFA is limited because the LO (a Quantum Cascade Laser) can only be tuned in discrete steps.
The GREAT sensitivities and integration times are calculated with the SOFIA Instrument Time Estimator (SITE). Presented here are the background of these calculations and some worked out examples. Because of the way a heterodyne receiver is calibrated (by measuring the receiver temperature, T_{rx}, with a hot and a cold load), the logical intensity unit for a heterodyne observation is temperature, expressed in Kelvin (K). Either the antenna temperature, T_{A}^{*} (the asterisk refers to values after correction for sky transmission, telescope losses and rearward spillover, see e.g. Kutner and Ulich, ApJ, 250, 341 (1981)) or the main beam brightness temperature, T_{mb}, are used. Similarly, the noise is expressed in temperature units as well, ΔTA * or ΔT_{mb}, and the sensitivity (or signal-to-noise ratio) of the observations is given by the ratio of the source temperature and the rms temperature of the spectrum. In order to calculate these quantities, we first must estimate the single sideband (SSB) system temperature, T_{sys}, which also includes losses from the atmosphere and the telescope. T_{sys} is given by:
(Eq.6-1)
T_{sys} = 2 x [T_{rx} + η_{telJ} x T_{sky} + η_{tel} x T_{s} + Tt_{el} ] /( η_{tel} x η_{sky})
The factor 2 in Equation 6-1 assumes that the noise temperature is the same in both signal and image band, which is true for the HEB mixers used by GREAT. The transmission of the atmosphere, η_{sky}, at the altitude, observing frequency, and airmass that we plan to observe at can be estimated using the atmospheric transmission code ATRAN. The GREAT time estimator calls ATRAN directly, so those estimating the integration time needed by using the time estimator have no need to run ATRAN separately. T_{sky} depends on η_{sky} and the ambient temperature of the sky (T_{amb}) where the signal is absorbed and can be derived from Equation 6-2.
(Eq. 6-2)
T_{sky} = J(T_{amb}) x (1 - η_{sky})
where J(T_{amb}) is the mean Rayleigh-Jeans (R-J) temperature of the atmosphere, which we assume to have a physical temperature of 220 K at 41,000 ft, resulting in J(T_{amb}) = 177.5 K at 1.9 THz. Likewise the telescope temperature, T_{tel}, is related to η_{tel} by Equation 6-3:
(Eq. 6-3)
T_{tel} = J_{tel} x (1 - η_{tel})
where J_{tel} is the radiation temperature of the telescope, with a physical temperature ~ 230 K (J_{tel} = 187.4 K at 1.9 THz). If we assume an η_{tel} of 0.92, then T_{tel} = 14.8 K.
As an example, let us calculate the system temperature at the [CII] fine structure line at 157.74 μm (1.9005369 THz). In this example we calculate what we would have at the beginning of a flight, when we are still at low altitude. We therefore assume that we fly at an altitude of 39,000 ft and observe at an elevation of 30 degree. For a standard atmospheric model this corresponds to a transmission of ~ 76%, which gives T_{sky} = 42.6 K. For a receiver temperature T_{rc} = 1100 K, Equation 6-1 therefore predicts a single sideband system temperature T_{sys} = 3301 K when observing the sky.
Now we are ready to calculate the sensitivity. The rms antenna temperature, (corrected for the atmospheric absorption, and telescope losses), ΔT_{A}^{*}, for both position switching
and beam switching is given by Equation 6-4
(Eq. 6-4)
ΔT_{A}^{*} = (2 x T_{sys} x κ ) x (t x Δν)^{-0.5}
where k is the backend degradation factor, t is the total integration time of the number of on and off pairs that we plan to take, and Δν is the frequency resolution of our spectra. Strictly speaking, Δν is the noise bandwidth, which can be slightly different than the frequency resolution, depending on the design of the spectrometer. For our example we expect the Full Width Half Maximum (FWHM) of the line to be a few km/s, and we will therefore calculate the rms for a velocity resolution of 1 km/s, corresponding to a frequency resolution of 6.3 MHz. Since the GREAT backends have much higher resolution, this is not a problem. We can easily bin the spectrum to our desired velocity resolution. For an observation with three pairs of 40 seconds in each beam, or t = 4 min, and assuming the backend degradation factor k=1, we then find ΔT_{A}^{*} = 0.17 K, which is the one sigma rms antenna temperature.
To convert antenna temperature to brightness temperature T_{R}^{*}, we have to make one more correction as shown in Equation 6-5:
(Eq. 6-5)
T_{R}^{*} = T_{A}^{* }/ η_{fss}
where η_{fss} is the forward scattering efficiency, usually measured for a very extended source (like the Moon). For GREAT η_{fss} = 0.97. Therefore our brightness rms temperature, ΔT_{R}^{*} = 0.18 K^{5}. Note: The GREAT time estimator assumes the line temperature in T_{R}^{*}, and not in main beam brightness temperature, T_{mb} = T_{R}^{*}/η_{MB} , which is for a source that just fills the main beam.
If we want to express our results in flux density, Sn, rather than brightness temperature, we can convert antenna temperature, T_{A}, to flux density, S_{ν}, using the standard relation given in Equation 6-6:
(Eq. 6-6)
S_{ν} = 2 x κ x η_{fss} x T_{A}^{* }/ A_{eff}^{ }
where κ is the Boltzmann constant, and A_{eff} is the effective area of the telescope. A_{eff} is related to the geometrical surface area of the telescope, Ag, by the aperture efficiency, η_{a},
i.e. A_{eff} = η_{a} x A_{g}. For the measured main beam efficiency in early April 2013 (0.67) and a Half Power Beam Width (HPBW) of ~ 14.1 arcsec (+/- 0.3 arcsec) an aperture efficiency^{6} of 55 +/- 2 % is derived. Equation 6-7 yields the following simple form for the 2.5 m SOFIA telescope:
(Eq. 6-7)
S (Jy) = 971 x T_{A}^{* } (K) or within errors ~ 1000 x T_{A}^{* }(K)
Normally we use Jy only for spatially unresolved sources, but we can also use Equation 6-7 to convert line intensities into W/m^{2}, which maybe a more familiar unit for the far infrared community. If we assume that the [CII] line we are observing is a Gaussian with a Full With Half Maximum (FWHM) of = 5 km/s, i.e. 31.8 MHz, the integrated line intensity is given by 1.065 x T_{peak} x Δν, where Δν = 31.8 MHz. If we take T_{peak} equal to our rms antenna temperature, we find using Equation 6-7 that our four minute integration therefore corresponds to a one sigma brightness limit of ~ 6.1 10-17 W/m^{2} for a 5 km/s wide line observed with 1 km/s resolution. If we only aim for a detection, we can probably degrade the resolution to 2 km/s. In this case we gain a square root of 2, and therefore our one sigma detection limit is 4.3⋅10^{-17} W/m^{2}.
This is the reverse of what is typical when writing a proposal, when the proposer has an estimate how wide and how bright the line is expected to be and knows what signal to noise is needed for the analysis. Assume we want to observe the [CII] 158 μm line in T Tauri, a young low-mass star. Podio et al. (2012, A&A, 545, A44) find a line intensity of 7.5 ⋅10^{-16} W m^{-2} for the Herschel PACS observations, which are unresolved in velocity (the PACS velocity resolution is ~ 240 km/s for [CII]). Here we want to velocity resolve the line to see if it is outflow dominated or whether it is emitted from a circumstellar disk or both. We therefore need a velocity resolution of 1 km/s or better. If we assume that the line is outflow dominated with a FWHM of say 20 km/s (127.2 MHz; little or no contribution from the circumstellar disk) we get a peak antenna temperature (using Equation 6-7) of 0.52 K or a radiation temperature T_{R}^{*} = 0.55 K. In this case we want a SNR of at least 10 and a velocity resolution of 1 km/s or better. Let’s check whether it is feasible. If we plug in the values we have in the GREAT time estimator (assume 40 degrees elevation, standard atmosphere, and we fly at 41,000 ft) or we can estimate it from the equations given above.
With these assumptions ATRAN gives us an atmospheric transmission of 0.86 integrated over the receiver band-pass. The receiver temperature is 1100 K (DSB). Using Equation 6-2, we find that the sky only adds 24.9 K to the system temperature and from Equation 6-1 we therefore get T_{sys} = 2881 K. Since we want to reach a signal to noise of 10, the rms antenna temperature ΔT_{A}^{*} = 0.052 K. We can now solve for the integration time using Equation 6-4, where we set Δν = 6.338 MHz (1 km/s resolution). In this case t = 1937 sec or 32.3 min. The PACS observations show the emission to be compact, so we can do the observations in Dual Beam Switching Mode (DBS; see Section 6.2.1.1), with a chop throw of 60 arcsecond. Both DBS and Total Power (TP) modes are currently estimated to have an overhead of 100% and a setup time for tuning and calibration of two minutes (which get added when entering the observations in USPOT, the SOFIA proposal tool). Our observation would therefore take 60 minutes, which is completely feasible. SITE gives t = 1930 sec. The difference is negligible.
Sensitivity calculations for an On-the-Fly (OTF) map, when data are taken while the telescope is scanning), are done a bit differently. For example, for an OTF map of the [CII] line (Half Power Beam Width, HPBW ~ 14 arcsec), we need to sample the beam about every 7 arcsec. If we read out the average once per second, for example, this means that we scan with a rate of 7 arcsec/second. To do a 3 arcmin scan will therefore take 26 sec, resulting in 26 map points, let us make it 27, to get an odd number of points. We therefore need to spend (1 second) * (√27) = 5.2 seconds on the reference position in total power mode. We ignore the time it takes the telescope to slew to the next row and any time needed for calibration. For a 3 x 3 arcmin^{2} map, i.e. 27 x 27 positions with a cell size of 7 x 7 arcsec^{2}. The integration time for each row is therefore 5.2 +27 seconds or 32.2 seconds/row. The total integration time for the map is therefore 14.5 minutes. We definitely want to do one repeat, so the total integration time is therefore 29 minutes. For all observing modes, we assume a 100% overhead and 2-minute setup for tuning and calibration. The total duration of the two maps is therefore 61.9 minutes. Thus, a 3 x 3 arcmin^{2} map in the [C II] line is entirely feasible.
Our 3 by 3 arcmin^{2} map with one repeat has an integration time of 2 seconds per map point. For typical observing conditions (41,000 feet, 30 degrees elevation) the GREAT time estimator (settings: TP OTF map, Non=27, Classic OTF; see Section 6.2.3) gives us an rms temperature/map point of 0.9 K for a velocity resolution of 1 km/s.
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This section describes the GREAT instrument and the available observing modes. It also contains the information required to estimate observing times in individual modes and examples of each.
If the frequency of interest has not already been used by GREAT, please contact the GREAT team to ensure that observing the line is feasible. 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 6.2.1.3 for details.
Two main observing modes are currently offered: Total Power (TP) and Beam Switching (BSW), the latter of which is available in either Single Beam Switching (SBS) or Dual Beam Switching modes (DBS).
GREAT offers four standard methods of observation through Astronomical Observation Templates (AOTs) in USPOT: Single Point, Raster Mapping, On the Fly (OTF) Mapping, and OTF Array Mapping. Each AOT is run in either Total Power or Beam Switching mode.
The spectroscopic stability (Allan variance) sets limits to the operation of a heterodyne instrument like GREAT.
BSW mode typically operates with 2.5 Hz, and therefore limitations are mainly set by the atmospheric stability and long integrations are typically performed. As such, integrations with 30 sec phase times are typically implemented for Single Point and OTF observations to achieve optimum spectroscopic stability. For weak and/or broad-line projects, DBS is recommended. No noticeable performance degradation has been observed from using SBS instead of DBS for other projects.
If TP mode observations are requested, the situation becomes complicated and multi-dimensional: science with linewidth more than a few 100 MHz and position changes greater than 10-15 arcmin between the ON and OFF positions become increasingly difficult, though not impossible. The actual impacts will depend on frequency, weather conditions, stability of the sky, elevation of the observation, and on the detector used. Contact a GREAT Instrument Scientist to discuss possible mitigations and their impact on the overheads to be assumed.
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 SITE. SITE is also useful to determine in which sideband the line of interest is best put, taking into account the atmospheric transmission. System temperatures for the line in the USB or LSB are given, as well as a plot showing the line locations for either LO tuning in comparison with the atmospheric transmission.
The time estimator calculates the time required to reach an rms brightness temperature ΔT_{R}^{*} , (T_{R}^{* = }T_{A}^{*}/ η_{mb}, where η_{mb} is the forward scattering efficiency and equal to 0.97 for GREAT at all bands) for a line at a frequency ν by solving the standard radiometric formula for a single point.
ΔT_{A}^{* }= (2T_{sys}) / (tΔν)^{0.5}_{ }
Here, ΔT_{A}^{*} is the antenna temperature corrected for ohmic losses and rear spillover. T_{sys} is the single sideband system temperature outside the earth's atmosphere, t is the integration time and Δν is the desired frequency resolution. This formula applies when t_{ON} = t_{OFF} , as is the case for single point total power observations, and all beam-switched observations.
For Total Power OTF mapping observations the corresponding equation is
T_{A}^{* }= T_{sys} (1 + (1 / N_{on})^{0.5})^{0.5} / (t Δν)^{0.5}
where t the ON-source integration time per map point only and Non is the number of on-source positions for each off-source observation.
The calculator uses the most recent measured receiver temperatures and calls the atmospheric transmission program ATRAN to estimate the atmospheric transmission for a given frequency, altitude, telescope elevation and water vapor overburden. The transmission is used to calculate T_{sys}, assuming an ambient temperature of the atmosphere of 220 K and a telescope temperature of 230 K.
GREAT is a dual sideband receiver, meaning it receives signal in two frequency bands, the upper sideband (USB) and the lower sideband (LSB). The transmission plot shows the location of both sidebands (separated by +/- 1.5 GHz for the LFA, HFA, and 4GREAT bands 3 and 4, and +/- 5.5 GHz for 4GREAT bands 1 and 2). It is possible to put the line to be observed in either the USB or the LSB (the two possible tunings). Integration times are calculated for both tunings. If the transmission is poor at the lower frequency but very good at the higher frequency, you would tune your line to the lower sideband. If the opposite is true you would tune your line to the upper sideband (USB).
Description of SITE Input Paramters
Type of Observation
Select "Single Point or Beam Switch OTF/Raster Map" for single point observations in both total power and beam-switched mode, and OTF/Raster map 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 you want in your 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 t he number of on positions (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). With the 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: HFA: 3 arcsec, LFA: 6 arcsec, 4GREAT1: 25 arcsec, 4GREAT2: 12 arcsec, 4GREAT3: 8 arcsec, 4GREAT4: 5 arcsec. 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 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 ON-source time per map point. Otherwise, enter the ON+OFF integration time. The time estimator will calculate the 1-sigma rms sensitivity (in units of T_{R}*) based on the input integration time.
Brightness Temperature T_{R}^{*} (K)
Enter the estimate of the peak brightness temperature of your line. This ﬁeld only appears 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 brightness temperature T_{R}^{*}. This relates to the measured antenna temperature as T_{A}^{* = }T_{R}^{*}η_{fss} and the main beam temperature (corrected for losses in the side lobes) as T_{MB} = T_{R}^{*}/η_{mb} . The main beam efﬁciency has been measured from planetary observations and determined to be 0.70 for the LFA, 0.63 for the HFA. For the latest 4GREAT main beam efﬁciencies, please contact the Help-Desk. A detailed description of the GREAT intensity calibration is given in Section 6.1.2.2, which also contains worked examples for different observing modes and unit conversions.
Source Velocity
Enter the source velocity (in km/s) in the 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 and the time estimator will calculate the observer velcity for you. 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 and your source is blue or redshifted to move you out of the atmospheric feature.
In general, OTF schemes are flexible and the detailed map parameters will depend on the goals of the project. The two OTF mapping options for upGREAT are the classic OTF (which can be used with the upGREAT arrays or the single-pixel GREAT channels) and OTF Array (which can only be used with the LFA or HFA).
Both AOTs can be executed as either Beam Switching mode or Total Power mode. Some things to consider when deciding between these two modes are:
Because upGREAT maps can be rotated relative to standard sky coordinates (e.g., J2000), they have their own coordinate system, defined by 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). Map rotation angle increases in the counter-clockwise direction, and the map angle can range from -360° to +360°. Scans in the x-direction are parallel to the x-axis, and scans in the y-direction are parallel to the y-axis.
The upGREAT Low Frequency Array (2x7 beam, H and V polarizations) 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 independent of scanning direction for maximum flexibility of observation planning.
When creating a mapping strategy, observers will have to weigh many factors, including the area to be mapped, the required integration time per point, and of course the scientific objectives. Examples given in Section 6.2.3.2 result in fully (or overly) sampled maps of the central region, but require different amounts of time to complete, and have very different integration times and coverage outside of the central region. In the Section 6.2.3.2a, a point in the central region may be mapped by only a few pixels, while in the Section 6.2.3.2b, the entire central region is mapped by each pixel . These are all important pieces of information to consider when planning mapping observations with upGREAT.
The classic OTF mapping is possible with either an upGREAT array or a single-pixel channel, and is the only OTF mapping option with a single pixel. In classic OTF mapping, each pixel makes a rectangular map based on the step size along the scan row, and the spacing between the scan rows. In the case of an upGREAT array, the result is seven rectangular maps; the amount of overlap between the maps depends on the map parameters (see Section 6.2.3.2a). In the case of a single-pixel GREAT channel, the result is a single rectangular map (see Section 6.2.3.2b).
In this example, we design an observation using the LFA such that the final map is composed of 14 fully sampled maps (one from each of the 2x7 pixels) of the central region. To ensure that all pixels cover the central region of the map during each scan, the scans start and end ½ of the array width before and after the central region in the x (RA) direction.
In addition, the top of the array is aligned with the bottom of the map, and each subsequent row is one step size (~6 arcseconds for the LFA) above the prior one (see Fig. 6-4). We use a 6 arcsecond step size along the row, which will result in a fully sampled map. We continue to make rows until the bottom of the array is aligned with the top of the map.
For this map, a scan length of 140 arcsec is sufficient to cover the central region and half of the array width before and after the central region. This scan length is also an multiple of the step size, which is a requirement for upGREAT maps. Based on the selected scan length and step size, each scan will have 20 points. Here we again select an integration time of 1 second per point, so each scan will take 20 seconds. The off position will require √20 ≈ 4.5 seconds, for a total of 24.5 seconds per scan. The entire map (including starting the map half of the array width below the central region and ending the map ½ of the array width above the central region) is made up of 20 rows. Thus, the total on+off time for the entire map is 490 seconds; after including a factor of 2 for overhead, the whole map takes about 17 minutes. Every point within the central region would have an integration time of 14 seconds (the combination of 2 polarizations x 7 maps, one for each pixel, with an integration time of 1 second each).
Note: In this example, if the other channel used for observing is a single pixel, a rectangular map will be created in this channel as well. Whether or not this map is fully sampled will depend on the frequency of the other channel and the step size used in the map.
In this example, we want to make a fully-sampled map of the filamentary cloud shown in Fig. 6-5 using L1, a single pixel channel. For this map, a rectangle of ~240 arcsec by ~128 arcsec, rotated by an angle of 45 degrees CCW, would cover the area of interest. If we select a step size of 8 arseconds, which would result in a fully-sampled map, we could scan in the long direction, with 30 (240 arcsec / 8 arcsec/dump) dumps along the scan row and 16 rows (128 arcsec / 8 arsec between rows). To keep the scan duration within 30 seconds, we select a dump time of 1 second per point. The off position will require √30 * 1 second ≈ 5.5 seconds, for a total of 35.5 seconds per scan. Thus, the total on+off time for the entire map is 568 seconds; after including a factor of 2 for overhead, the whole map takes about 19 minutes. Every point within the map would have an integration time of 1 second.
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. 6-6). For both the LFA and the HFA, the projected pixel spacing (after rotating the array by -19.1°) 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 oversampled map), depending on the goals of the project.
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, scanning in both directions (Fig. 6-7). Scanning in both directions helps to minimize the striping effects that can be caused by the different characteristics of the array pixels.
Because of the flexibility of the mapping scheme, there can be multiple ways to observe the same region. For example, the two setups in Fig. 6-8 both fully cover the same area. Some important factors in determining the proper setup between these two options are the desired integration time per point, the step size between the points, and the duration of a single scan.
In this example, the rotated array makes four total scans—two in the x- (RA) direction and two in the y- (Dec) direction Fig. 6-9. Because the projected pixel separation of 11 arcsec is larger than the beam size at 1.9 THz (14 arcsec), two scans in each direction are required to fully sample the area. These scans are separated by 5.5 arcsec (1/2 of the projected pixel separation), resulting in a slightly oversampled map.
To ensure that all pixels cover a part of the central region of the map during each scan, the scans start and end ½ of the array width before and after the central region. To get evenly spaced sampling, we select a 5.5 arcsecond step size along the rows. This step size, along with the ½ array length added to the beginning and end of the scan, results in a total scan length of 143 arcseconds (26 steps).
If we select 1 second integration time per point, each scan will take 26 seconds, and the off integration for each scan will take √26 ≈ 5 seconds. Thus, for the 4 scans that comprise the map, the total on+off time will be approximately 125 seconds. Including a factor of two for overhead, the total time for this map would be a little over four minutes, and each position in the central region of the map would have an integration time of ~4 seconds (2 seconds from each polarization).
Note: In this example, if the other channel used for observing is a single-pixel, only an irregularly spaced map will be created in this channel. The shape of this will match the region traced out by the center array pixel.