The Far Infrared Field-Imaging Line Spectrometer (FIFI-LS) is an integral field, far infrared spectrometer. The instrument includes two independent, simultaneously operating grating spectrometers sharing one common field-of-view (FOV). Each spectrometer has a detector consisting of 400 pixels of Germanium Gallium-doped photoconductors. The short wavelength spectrometer (blue channel) operates at wavelengths between 50 μm and 125 μm, while the long wavelength spectrometer (red channel) covers the range from 105 μm up to 200 μm. One of two dichroics has to be selected for an observation affecting the wavelength range of both channels in the overlap region.
The projection onto the sky of the 5x5 pixel FOVs of both channels is concentric (10 arcsec offset), but the angular size of the FOVs differs. The red channel has a pixel size of 12x12 arcsec yielding a square 1 arcmin FOV and the blue channel has a pixel size of 6x6 arcsec, which yields a square 30 arcsec FOV.
The resolving power of both channels varies between 1000 and 2000 dependent on the observed wavelength. The higher values are reached towards the long wavelength ends of each spectrometer.
The detectors are cooled down to about 1.7 K with super fluid helium. The spectrometers and all mirrors are cooled down to 4 K with liquid helium. The exception is the entrance optics featuring a K-mirror (see Section 126.96.36.199) and an internal calibration source. These optical components are cooled to about 80 K with liquid nitrogen.
The integral field unit (IFU) allows FIFI-LS to obtain spectra at each point in its FOV; this is in contrast to a spectrometer with a slit, which only provides spectra along the slit. Both channels in FIFI-LS have an IFU, which consists of 15 specialized mirrors to separate the two dimensional 5x5 pixel FOV into five slices (of five pixels length each) which are then reorganized along a (one dimensional) line (25x1 pixel). This line forms the entrance slit of the actual spectrometer. The diffraction grating disperses the incoming light in the spectral dimension. Finally the dispersed light reaches the 16x25 pixel detector array. The result is a data cube with 5x5 spatial pixels (spaxels) and 16 pixels in the spectral dimension. Figure 3-1 shows the concept.
Figure 2-6. Comparison of raw 2D spectra of EXES in the HIGH_MED (left) and HIGH_LOW (right) configurations obtained during commissioning flights. The spectra are not nod-subtracted, highlighting the sky emission lines (dark). This comparison shows that, while the HIGH_MED and HIGH_LOW configurations have the same spectral resolution, HIGH_LOW has a much larger spectral coverage at the expensive of a shorter slit to be able to pack more orders on the array. In contrast, the Low and Medium configurations (not shown) have the same spectral coverage as HIGH_LOW and HIGH_MED, respectively, but a lower spectral resolution without cross dispersion. The approximate start and end wavelengths are indicated in red.
The two channels have an overlap in their wavelength range. That is necessary because a dichroic splits the light between the two channels allowing the common FOV for both channels. The drawback is that a dichroic has a transition region where neither the transmission nor the reflection is good. Thus, FIFI-LS has two dichroics with transitions at different wavelengths. The The D105 cuts off the blue channel at about 100 μm and opens the red at about 115 μm. The D130 cuts off the blue channel at 120 μm and opens the red at 130 μm. Figure 3-2 should be used to choose the best dichroic and line combinations. The proposer needs to pair up wavelengths so that each pair can be observed efficiently with one of the dichroics. Typically, the D105 is used unless a wavelength between 100 and 115 μm is observed.
Figure 3-2. Throughput of optical system—here the transmission of the overall optical system is shown for the six possible optical configurations using two dichroic beam splitters (D105 and D130) and both grating orders (blue channel only).
The SOFIA telescope is essentially an Alt-Az-mounted telescope. Thus, the field of view on the sky rotates while tracking an object. However, the telescope can rotate around all three axes, but the amount it can rotate in cross-elevation and line-of-sight is limited. Thus, the normally continuous sky rotation is frozen-in for some time while the telescope is inertially stabilized. When the telescope reaches its limit in line-of-sight rotation, it needs to rewind, resulting in a rotated FOV of the telescope.
FIFI-LS has a beam rotator (K-mirror) that rotates the instrument's FOV, counteracting the sky rotation experienced by the SOFIA telescope. When a rewind happens, the FIFI-LS beam rotator will automatically rotate the FOV of the instrument, so that the position angle of the instrument's FOV on the sky is maintained. An additional benefit is that the beam rotator enables the observer to line up the FOV with e.g. the axes of a galaxy and keep the alignment. The desired position angle of the FOV can be specified in Phase II of the proposal process.
The FIFI-LS design is very similar to the Herschel/PACS-spectrometer sharing much of the design. The detectors are basically the same and the optical design is very similar (same sized gratings in Littrow configuration, same IFU). The difference is that FIFI-LS features two grating spectrometers whereas the PACS-spectrometer had only one. The two gratings make it possible to observe two different wavelengths simultaneously and independent of each other (one in each channel). This design also allows different pixel sizes (6 arcsec vs 12 arcsec) in each spectrometer, which means a better match to the beam size. The spectral range of FIFI-LS also goes down to 51 μm whereas PACS did not routinely observe the [OIII] 52 μm line.
The blue spectrometer operates in 1st and 2nd order. An order-sorting filter blocks the unwanted order. The red spectrometer only operates in 1st order. The spectral resolution of FIFI-LS depends on the observed wavelength. It ranges from R = λ/Δλ ~500 to 2000 corresponding to a velocity resolution of 150 to 600 km/s. The top panel of Figure 3-3 shows the spectral resolution in velocity and in R vs. wavelength, also given in Table 3-1 for selected spectral lines.
FIFI-LS has 16 pixels in the spectral direction. The wavelength range covered by these 16 pixels also depends on the observing wavelength. The bottom panel of Figure 3-3 shows the instantaneous spectral coverage or bandwidth (BW) in micron.
Rest λ (micron)
Inst. Cov. (km/s)
Inst. Cov. (micron)
Rest λ (micron)
Inst. Cov. (km/s)
Inst. Cov. (micron)
more to come CO lines
Spectral resolution and instantaneous coverage for selected spectral lines
Figure 3-3. Top, The spectral resolution in km/s and λ/Δλ for both channels; Bottom, The instantaneous wavelength coverage in km/s of the 16 spectral pixels vs. wavelength.
FIFI-LS will operate such that the detectors are always background-limited, infrared photodetectors. Under this assumption, the overall performance of FIFI-LS as a function of wavelength has been estimated. Further assumptions about the emissivity of the telescope, optics, and baffling, the efficiency of the detectors had to be made. Figure 3-4 shows the resulting sensitivities for continuum and unresolved lines as minimum detectable fluxes per pixel, i.e. detected with a signal to noise ratio (SNR) of 4 and an on-source integration time of 900 s or 15 min.
The SOFIA Instrument Time Estimator (SITE) should be used to estimate the on-source exposure times used in proposals and observing preparation. The time estimator calculates the on-source integration time per map position for a source flux, F and a desired SNR using Eq. 3-1:
where MDF(λ) is either the Minimum Detectable Continuum Flux (MDCF) in Jy per pixel or the Minimum Detectable Line Flux (MDLF) in W m-2 per pixel at the entered wavelength (see Figure 3-4).
Figure 3-4. Continuum and emission line sensitivities for a monochromatic point source: The values are calculated for a SNR of 4 in 900 s. The MDCF is in Jy per pixel and the MDLF is in Wm-2 per pixel. Both sensitivity values scale as SNR / √(t), where t is the on-source integration time.
The high sky background in the far infrared requires careful subtraction. That is achieved by chopping with SOFIA's secondary mirror and/or by nodding the telescope.
In the chopped modes (symmetric and asymmetric chop) the secondary chops at 2 Hz to efficiently remove the sky emission. To remove residual background not canceled by chopping, the telescope is nodded typically every 30s either to move the source to the other chop-beam or to an off-position. Since the instrument telescope communications and the telescope move take 8s, a whole nod-cycle for a symmetrically chopped observation typically takes 76s. In the unchopped modes (OTF and total power) integration times vary between 10 and 30s to ensure a sufficiently short nod interval.
Symmetric chopping is the most commonly used observing mode with FIFI-LS since it combines the best background subtraction offered by chopping with good observing efficiency. Asymmetric chopping becomes necessary for extended sources but does also allow for shorter on source integration times for bright sources. Total Power observations are used for even larger sources that do not enable chopping at all. On the fly mapping (OTF) is a new mode that that enables good spatial sampling and observing efficiencies for extended maps.
The following sections describe the possible observing modes. In the discussion of the overheads, N is the number of map positions and ton is the on-source exposure time per map position. Details like the exact chop throw and angle do not need to be fixed until Phase II of the proposal process, but proposers should attempt to determine if their chosen mode is feasible for their targets as moving to a different mode, often with a higher overhead, after time has been allocated can give less integration time on the targets and thus affect the feasibility of the program. Information on how the parameters for each mode is to be entered into USPOT during Phase II of the proposal process can be found on the FIFI-LS USPOT web page.
This mode combines chopping symmetrically around the telescope's optical axis with a matched telescope nod to remove the residual telescope background. This mode is also known as nod match-chop (NMC) (cf. Section 5.2.1) or beam switching (BSW, cf. Section 7.2.1).
When observing using a symmetric chop the target is imaged off the optical axis. Large chop amplitudes therefore degrade the image quality due to the introduction of coma. This effect causes asymmetric smearing of the Point Spread Function (PSF) in the direction of the chop. However, the effect is small (with an effect on the Signal to Noise Ratio (SNR) of less than 10%) in the red channel for all permitted chop throws and in the blue channel for total chop throws less then 6 arcmin and wavelengths longer than 63 μm. For wavelengths shorter than 63 μm, we recommend total chop throws of less than 4 arcmin, although observations have been made successfully with larger throws – please contact the SOFIA helpdesk (firstname.lastname@example.org) to discuss this if it is necessary for your observations. Generally, it is recommended to use a chop as small as possible while keeping the FOV in the off positions outside of any detectable emission.
The position angle of the chop can be specified relative to equatorial coordinates or telescope coordinates (e.g. horizontal). Keep in mind that the telescope nod matched to the chop creates two off-positions symmetric to the on-position (Figure 3-5). Horizontal chopping is preferred when it is possible, i.e. for relatively small sources without any other sources of emission in the surrounding field and for which the position angle of the chop is thus unimportant.
The total overhead in this mode is about 1.6 N ton + 300s, since the source is only observed during 50% of the observation and additional time is required for telescope moves, plus 300s for the setup. This overhead estimate assumes that the on-source exposure time per map position ton is 30s; ton can be set to any value between 15 and 30s in this mode but for values less than 30s the overhead calculated by USPOT will be larger than given here as the fixed time for the telescope moves becomes more important. If the desired on-source exposure time per map position ton is less than 15s, the asymmetric chop mode or the on the fly mapping mode should be used.
Figure 3-5. The geometry of chopping and nodding in the Symmetric Chop mode (left) and the Asymmetric Chop mode (right).
If the target's size or environment does not allow the Symmetric Chop mode to be used, e.g. if it is not possible to find clean symmetric chop positions on opposite sides of the source, the Asymmetric Chop mode allows larger chop throws and needs an emission free field only in direction from the source. The maximum chop throw is ~10 arcmin for all wavelengths. It also allows for faster mapping of extended sources. The asymmetric chop keeps the on-beam on the optical axis in most cases, resulting in an image unaffected by coma. Consequently, the off-beam is off-center by twice the amount of a symmetric chop with the same chop throw, resulting in twice as much coma in the off – but as the off-beam should only see empty sky this does not affect the observations. The telescope is nodded to an off position where the same chopped observation is executed to provide the residual background subtraction. Figure 3.5 illustrates this geometry.
The ’classical’ asymmetric chop uses an ABBA nod pattern, for most cases a modified ABA nod pattern, which is the default in this mode, is recommended, For the fastest mapping an AABAA nod pattern is available. In both of these modified nod patterns, the B (off) nod is longer than the individual A (on) nods. For the ABA pattern, the B is 1.5 times the length of the A and for the AABAA pattern the B is 2 times the length of the A. These modified nod patterns are beneficial on very bright objects, where the estimated on-source exposure time per map position is 15 s or less so that the total observing time is dominated by telescope movements. The actual patterns are thus ABA′ and AA′BA″A‴, i.e. the A positions are all different. In this mode, the total overhead is 3.3 N ton + 300s assuming an on-source exposure time per map position of 15s for the ABA pattern and 3.0 N ton + 300s, assuming an on-source exposure per map position of 10s for the AABAA pattern. The overhead increases with shorter integration times, thus USPOT may return different overheads from those given here if different observing times are used. These modified nod patterns should also be used for any source with asymmetric chop as long as the line is narrow enough to fit within the instrument's instantaneous spectral coverage.
If the line is very wide the ‘classical’ mode has to be used. Here the total overhead in this mode is about 4.1 N ton + 300s, since the source is observed during 25% of the observation plus additional time for telescope moves and 300s for the setup. This overhead estimate assumes that the on-source exposure time per map position ton is at least 15s.
Sometimes the target’s environment does not allow even a single chop position to be used, in these cases it is still possible to make observations of bright targets using the unchopped Total Power mode. This uses the same ABA pattern used for the asymmetric chop mode above but without any chop being made. This can lead to potentially poorer background subtraction as the only off-source position is the B nod, so there is some additional risk. In stable atmospheric conditions it can give results as good as the symmetric chop mode. In this mode, the total overhead is 1.9 N ton + 300s assuming an on-source exposure time per map position of 10s.
The On The Fly Mapping (OTF) Mode can be used to map large areas of bright emission efficiently. This is a new mode that is still undergoing commissioning and development so is offered as shared-risk observing only. Overhead and sensitivity calculations may change so observers should be conservative when estimating the observing time needed for this mode.
In OTF mode, the telescope is driven across the source, taking data ‘on the fly’. No chopping is done, so the same caveats that apply for the total power mode (above) apply to OTF. An ‘off’ nod position is taken at the end of each scan through the source, with a time of √N tsample, where N is the number of independent samples in the scan and tsample is the integration time for each of these samples. This off is used for all of the samples in the scan.
Each scan takes 30s and the length is determined by the scan speed. The map is built up by scans spaced by the width of the array being used (30” for blue, 60” for red) and (if desired) by crossing scans at right angles. As this mode is still under development, potential users should contact the helpdesk (email@example.com) to discuss their planned observing strategy prior to submitting a proposal.
In contrast to the other observing modes, this mode targets spectral features much wider than the bandwidth (see Section 188.8.131.52) like solid state features. The problem is a good atmospheric calibration over the whole observed wavelength range. The spectrum has to pieced together from many different exposures. The best way to take such data and how to reduce it is still being investigated. If this observing mode is considered, the Help-Desk must be contacted well in advance to allow for time to calculate overheads.
The SOFIA Instrument Time Estimator (SITE) should be used to estimate the on-source exposure times used in proposals and observing preparation. The time estimator requires the following input:
Wavelength (in microns, between 51 and 203 μm): default 157.741 μm (rest wavelength of the [CII] line) Specify the rest wavelength of the requested transition.
Bandwidth (in km/s or microns): default 0 km/s Enter the desired width of the spectrum. The width should allow for sufficient baseline on both sides of the expected line/spectral feature to allow a good estimate of the underlying continuum telluric and astronomical. This value enters the time estimate as the factor l. If the desired spectrum is wider than the instantaneous bandwidth, I is the ratio of the requested width of the spectrum and the bandwidth (Figure 3-3). Otherwise I is equal to 1.
Observer Velocity (VLSR in km/s): default 0 km/s In many cases, the default value of zero can be used. However, if the observing wavelength is near a strong narrow telluric feature, the Earth's velocity relative to the LSR becomes important, e.g. for galactic sources and the [OI] line at 145.525 μm. Then either enter the velocity directly or have it computed by entering time, date, source coordinates, and SOFIA's location (boxes for these are shown if Compute Velocity is checked). The Doppler-shift due to the source's and the observatory's velocity is important to estimate the atmospheric extinction, discussed further below.
Signal to Noise Ratio or Total Integration Time (s) default S/N ratio resulting from a Total Integration Time of 900 s SITE can either calculate the resulting signal to noise ratio given an integration time or the integration time to reach a signal to noise ratio. Select one of these parameters to be calculated and specify the value of the other parameter. For continuum observations, SNR is based on averaging over the entire spectrum.
Astronomical Source Definition
Source Flux default 2.087e-17 W m-2 line flux (MDLF per pixel for [CII]) Specify the expected source flux per FIFI-LS pixel either as integrated line flux in W/m2 or as continuum flux density in Jansky and select ‘line’ or ‘continuum’ as appropriate. Make it obvious in the technical feasibility section of the proposal that the referenced flux estimates have been converted to FIFI-LS pixels sizes.
Source Velocity (in km/s): default 0 km/s Enter the radial velocity of the source relative to the local standard of rest (LSR).
Observing Condition Constraints
Elevation Angle (20, 40 or 60 deg): default 40 For northern sources an elevation of 40° is okay, but sources south of a declination of -15° will most likely be observed at a respectively lower elevations unless an observation from the southern hemisphere is required.
Altitude (in feet; 35 – 45,000 ft): default 41,000 ft This value is used in ATRAN to derive the atmospheric absorption. For more details about ATRAN see Section 1.3. On a typical SOFIA flight, observations start at 38,000 ft or 39,000 ft and 43,000 ft are reached 3.5 h before the observations end. The default value of 41,000 ft represents an average altitude. If you want to be conservative, using a value of 38,000 ft should ensures that time estimate does not underestimate the water vapor overburden. If an observation is rather sensitive to the water vapor, a higher altitude can be entered and justified in the proposal. In Phase II, select Low or Very Low for Requested WV Overburden in the Observing Condition panel in USPOT, if the altitude used in the time estimation is 41,000 ft or 43,000 ft, respectively. Note, that this limits the schedulability of the observation to the last 5.5 h or 3.5 h of observations.
Zenith Water Vapor Overburden (in microns) This is automatically set to a typical value for the altitude selected, e.g. selecting an altitude of 39,000 ft will set the water vapor to 9.6 microns.
The time estimator calculates the on-source integration time per map position for a source flux, F and a desired SNR using Eq.3-1 (see also Figure 3-4).
The factor α is the transmission of the atmosphere for the observing wavelength derived by ATRAN. The on-line time estimator includes a plot of the transmission of the atmosphere at full spectral resolution and smoothed to the spectral resolution of FIFI-LS at the observing wavelength over the bandwidth. Two integration times are calculated using the transmissions from each curve. The value derived from the unsmoothed curve applies to an observation of a very narrow line, while the value from the smoothed curve applies to a continuum source or a line broader than the instrument's spectral resolution. If the atmospheric transmission is smooth near the observing wavelength, the two values will not differ much and the more conservative or appropriate observing time should be chosen. Furthermore, the observing time will not depend strongly on the source velocity. The velocity correction can be rounded to 100km/s and the earth's velocity can be ignored.
However, if there is a telluric feature near the observing wavelength, one has to carefully check the feasibility of the observation (a special warning is displayed if the ratio of the derived observing times exceed 1.5). This usually happens when the observing wavelength is near a strong and narrow atmospheric feature. A typical example is the [OI] line at 145.525 μm, which is near a narrow and strong telluric feature at 145.513 μm or at -25 km/s relative to the [OI] line. In such a case, it is crucial to enter a good estimate of the source velocity accurate to ~1 km/s. The source velocity needs to be the combination of the source velocity relative to the LSR or another reference frame and earth's velocity relative to that reference frame, which depends on the observing date and target location. Therefore the time estimator includes a calculator for the earth's velocity relative to the LSR. It may be necessary to add a time constraint for the observation to avoid an adverse earth's velocity relative to the source.
If the observing line is near a strong and narrow telluric feature, not only the observing time estimate needs greater care, but the correction for the atmospheric absorption of an observed line flux will have a large uncertainty. To derive the correction factor, the atmospheric transmission curve would need to be integrated while weighted with the intrinsic line profile of the observed emission line with the correct relative Doppler-shift. In most cases FIFI-LS will not be able to resolve the line profile and cannot resolve the atmospheric feature. Any attempt to correct the measured line flux would depend strongly on assumptions of the source's line shape and position and assumptions of the water vapor content and shape of the telluric feature. In short, expect a large uncertainty of a line flux measured near a strong and narrow telluric feature.
The exposure time estimator returns the on-source exposure time per map positionton. If mapping is planned, this values has to be multiplied with N, the number of map positions, to derive the total on-source observing time. More on mapping can be found in Section 3.2.3. The total on-source observing time N x ton has to be entered into USPOTduring Phase I of the proposal process. The overhead depends on the observing mode (Section 3.2.3) and is automatically added by USPOT.
Be conservative with the time estimates! Unforeseen issues like thunderstorms or computer crashes may cut the observing time short. Better to aim for 5σ and get a 3σ result, than aim for a 3σ and then wonder, what to do with a 1.8σ signal.
Spectral dithering is always employed for self flat-fielding and increased redundancy. Spectral dithering implemented via a grating scan. The grating is moved in small steps, so that the spectrum moves over different pixels in the spectral dimension of the detector array.
The default pattern to cover the instantaneous bandwidth (BW, Section 184.108.40.206) is to move the grating 12 steps, each corresponding to half a spectral pixel width. This pattern results in a spectrum about 30% wider than the BW. The central 70% of the BW are observed during the whole observing time reaching the full SNR, while the remaining 15% on each side of the BW should reach on average 86% of the SNR. The SNR reached on the extra 30% should still be 46% on average based on the observing time for each part of the spectrum. For wider spectral coverage, the step size and number of steps of the grating scan will be adjusted by the instrument operators to achieve the desired spectral coverage. The steps will be evenly distributed over the nod-cycles.
Raster Mapping is supported by the Symmetric Chop, Asymmetric Chop and Total Power observing modes; OTF Mapping is a dedicated mapping mode that is covered separately below.
Raster mapping can be done on a rectangular grid with a user-defined spacing and extent. It is also possible to supply a list of mapping positions to achieve a map with a custom shape optimized to the source geometry. These details need to be specified only in Phase II of the proposal process (see the FIFI-LS USPOT chapter). In Phase I, the effective map area needs to be entered in USPOT and the proposal should explain the suggested mapping strategy. The on-source integration time per cycle entered in USPOT is the on-source integration time per cycle per raster point. This gives a total on-source exposure time for the AOR of this number multiplied by the number of raster map points Ncycle Npoint ton.
For chopped observations: If the source geometry allows the chopped beams to be positioned symmetrically on both sides of the source, then one should use the more efficient Symmetric Chop mode for mapping. If that is not possible the Asymmetric Chop mode has to be used; for short integrations, one of the modified nod patterns (ABA or AABAA) is preferred. Figure 3-6 illustrates mapping with an asymmetric chop. The chopped map (positions A1chop to A3chop in the example) covers an area with the same form as the on-source map, offset by the chop throw. If this is undesirable (e.g. if part of the chopped map would overlap a region of possible emission), the map needs to be broken up into sub-maps with varying chop parameters (which can be specified in Phase II). Breaking the map up into individual sub-maps requires a separate AOR for each map. If there are more than five AORs in a map, all with short integration times, it may be desirable to toggle the flag for combining multiple short AORs in USPOT, which enables an alternative calculation of overheads with a lower fixed overhead per AOR.
When estimating the on-source integration time (Section 220.127.116.11), take into account the differing overlap of the red and blue FOV at the desired raster map spacing. The SNR entered into the calculation of ton is the SNR for a single raster map point. The final SNR for a point in the map should reach √n * SNR with n being the number of raster points from which a point is covered by the respective FOV. For example in Figure 3-6, the area of the spaxel in the middle (dark orange) is covered by 3 FOVs while 16 spaxels (light orange) are covered by 2 FOVs and the outer parts of the map (yellow) are covered by 1 FOV. The noise level in the area covered by the central spaxel should thus be √3 lower than in the outer parts and the SNR (for the same signal) thus √3 times higher. (Note that this is an example map, not a suggested mapping strategy.)
Figure 3-6. The geometry of chopping and nodding while mapping using the asymmetric chop mode.
On The Fly (OTF) Mapping involves taking data while the telescope is in motion, in contrast to the hop-and-dwell approach of raster mapping where the telescope only moves between integrations. It allows fast, well-sampled maps to be made of bright, extended sources.
During an OTF scan the FIFI-LS field of view is rotated at 11.3 degrees to the direction at which the telescope is being driven, giving an equal spacing of the spaxels in the cross-scan direction. Combined with integrations of 1/8th of a second as the telescope moves, this builds up a dense array of points at which data have been taken giving a good sampling of the spatial PSF.
As each point is crossed by 5 spaxels, the effective integration time per spaxel (i.e. what should be put into SITE to estimate the SNR) is given by 5 * spaxelsize/scanspeed in each scan direction. For a standard 30s scan, the length of the scan (and thus the size of the map) is also given by the scanspeed. As the data is taken while the telescope is in motion, higher scan speeds could result in smearing of the beam in the direction of the scan.
An example OTF map is shown in Figure 3-7. This shows six scans (three in each direction) for the blue array with a speed of 4”/s (giving a scan length of 2’). The on-source time for this map is estimated as 6 * 0.5 = 3 minutes and the variable overhead as 1.5 * 6 * 0.5 = 4.5 minutes. Adding in the fixed overhead of 5 minutes gives a total time of 12.5 minutes. The integration time per spaxel (reached within the red box, covering 1.5’ by 1.5’) is 5 * 6”/4”/s = 7.5s in each scan direction, for a total of 15s. A map of this size would normally take 9 pointings. With an integration time of 15s/pointing this would take 16.4 minutes in symmetric chop mode (2.25 minutes on-source, 9.15 minutes variable overhead, 5 minutes fixed overhead), which would not give any dithering.