# 3.1   Specifications

## 3.1.1   Instrument Overview

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 3.1.1.3) and an internal calibration source. These optical components are cooled to about 80 K with liquid nitrogen.

### 3.1.1.1   Integral Field Concept

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 3-1.

Figure 3-1. Illustration of the field imaging concept in FIFI-LS. The optics slice the rows of the 5x5 pixel field of view into a 25x1 pixel pseudo slit.

### 3.1.1.2   Selection of the Dichroic

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.

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).

### 3.1.1.3   Beam Rotator

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.

## 3.1.2   Performance

### 3.1.2.1   Comparison with the PACS Spectrometer

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.

### 3.1.2.2   Spectral Resolution

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.

Table 3-1.
Line Rest λ (micron) Channel R FWHM (km/s) Inst. Cov. (km/s) Inst. Cov. (micron)
[OIII] 51.8 blue 950 320 1840 0.32
[NIII] 57.3 blue 1050 280 1540 0.29
[OI] 63.2 blue 1300 230 1240 0.26
[OIII] 88.4 blue 600 490 2340 0.69
[NII] 121.9 red 750 390 2340 0.69
[NII] 121.9 blue 1050 290 1350 0.55
[OI] 145.5 red 1000 300 1800 0.87
[CII] 157.7 red 1150 260 1560 0.82
more to come CO lines
Spectral resolution and instantaneous coverage for selected spectral lines

Figure 3-3.

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.

### 3.1.2.3   Sensitivity

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:

(Eq.3-1)

$ton=l(SNR/4αF/MDF(λ))2900 s$

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.

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.

# 3.2.   Planning Observations

## 3.2.1   Observing Modes

The high sky background in the far infrared requires careful subtraction. That is achieved by chopping with SOFIA's secondary mirror and by nodding the telescope. The secondary will chop at 2 Hz to efficiently remove the sky emission. To remove residual background not canceled by chopping, the telescope is nodded typically every 30 s 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 10 s, a whole nod-cycle takes typically 80 s.

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. The main driver to choose the observing mode is to figure out possible chop configuration. However, the details like the exact chop throw and angle and other observing details do not need to be fixed until Phase II of the proposal process. 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.

### 3.2.1.1   Symmetric Chop

If possible this observing mode should be used because it is the most efficient mode. This mode combines chopping symmetrically to 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) mode (cf. Section 5.2.1) or beam switching (BSW, cf. Section 7.2.1).

When observing using a symmetric chop, large chop amplitudes 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 effect on Signal to Noise Ratio (SNR) less than 10%) in the red channel for all 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. Generally, it is recommended to use a chop as small as possible, but keep 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).

The total overhead in this mode is about 1.6N ton + 300 s, since the source is only observed during 50% of the observation and additional time is required for telescope moves, plus 300 s for the setup. This overhead estimate assumes that the on-source exposure time per map position ton is at least 30 s. If the on-source exposure time per map position ton is less than 15 s, the Bright Object mode should be used. For values of ton in between, one needs to enter an alternate overhead in USPOT. The total alternate overhead is N(ton + 20 s) + 300 s.

Figure 3-5.

Figure 3-5. The geometry of chopping and nodding in the Symmetric Chop mode (left) and the Asymmetric mode (right).

### 3.2.1.2   Asymmetric Chop

If the target's size or environment does not allow to use the Symmetric Chop mode, one has to use the Asymmetric Chop mode allowing larger chop throws at shorter wavelengths and is not creating symmetric off-positions around the source. The asymmetric chop keeps the on-beam on the optical axis. This results in an image unaffected by coma. Consequently, the off-beam is off-center by twice the amount compared to the symmetric chop with the same chop throw resulting in twice as much coma. But that is of no consequence as the off-beam should only see empty sky. The telescope is nodded to an off-position where the same chopped observation is executed to provide the residual background subtraction. Figure 3-4 illustrates this geometry.

The total overhead in this mode is about 4.2N ton + 300 s, since the source is observed during 25% of the observation plus additional time for telescope moves and 300 s for the setup. This overhead estimate assumes that the on-source exposure time per map position ton is at least 15 s. For shorter values of ton, the Bright Object mode should be used.

### 3.2.1.3   Bright Objects

For very bright objects, where the estimated on-source exposure time per map position is 15 s or less, the total observing time is dominated by telescope movements. The efficiency of mapping such bright objects can be improved by observing two map positions and one off-position per nod-cycle using an asymmetric chop. In this mode, the total overhead is 3 N ton + 300 s assuming an on-source exposure times per map position of about 15 s. Please contact the Help-Desk, if you are planning shorter integration times. The overhead increases with shorter integration times and the standard overhead calculation should be overwritten with the actual overheads for such short integrations times. This mode can 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.

### 3.2.1.4   Spectral Scan

In contrast to the other observing modes, this mode targets spectral features much wider than the bandwidth (see Section 3.1.2.2) 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.

## 3.2.2   Integration Time Estimates

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:

Instrument Properties

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.

Calculation Method

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 position ton. 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 USPOT during 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.

## 3.2.3   Spectral Dithering

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 3.1.2.2) 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.

## 3.2.4   Mapping

Mapping is supported by all of the observing modes exept the Spectral Scan. It 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. For both map types, a spacing of 15 arcsec might be a good choice providing half pixel steps to yields super-resolution with a good overlap for the blue array and a very strong overlap for the red array. For very large maps fast maps, a spacing of half a red array or 30 arcsec achievs super-resolution with a good overlap for the red array and full coverage (but no overlap) for the blue array. 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 to be entered in USPOT has to be the on-source integration time per raster point multiplied by the number of raster map points N ton.

If the source geometry allows the off-beam to be positioned symmetrically on both sides of the source, then one should use the much more efficient Symmetric Chop mode for mapping. If that is not possible the Asymmetric Chop mode has to be used. An asymmetric chop is also used in the Bright Object mode. Figure 3-6 illustrates mapping with an asymmetric chop. The off-beam (positions B1 to B3) covers an area while chopping that is the same size as the map itself. If this is undesirable, the map needs to be broken up into sub-maps with varying chop parameters to be specified in Phase II. The availability of guide stars might be another reason to break up a large map into sub-maps. In this case the sub-maps will be identified between Phase II and the actual observation by the support scientist in close collaboration with the guest investigator and the telescope operator.

When estimating the on-source integration time (Section 3.1.2.3), 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 √x * 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 pixel in the middle is covered by 3 FOVs while 16 pixels are covered by 2 FOVs and the outer parts of the map are covered by 1 FOV.

Figure 3-6.

Figure 3-6. The geometry of chopping and nodding while mapping using the asymmetric chop mode.