# Characterization and Absolute Calibration of the Far Infrared Field Integral
Line Spectrometer for SOFIA

Dario Fadda Space Telescope Science Institute, 3700 San Martin Dr, Baltimore,
MD 21218, USA  Sebastian Colditz Deutsche SOFIA Institut, University of
Stuttgart, 70569 Stuttgart, Germany  Christian Fischer Deutsche SOFIA
Institut, University of Stuttgart, 70569 Stuttgart, Germany  William D. Vacca
Gemini Observatory/NSF’s NOIRLab, 670 N. A’ohoku Place, Hilo, Hawai’i, 96720,
USA  Jason Chu Large Binocular Telescope Observatory, 633 N Cherry Ave,
Tucson, AZ 85719, USA  Melanie Clarke Space Telescope Science Institute, 3700
San Martin Dr, Baltimore, MD 21218, USA  Randolf Klein Lockheed Martin Space,
Advanced Technology Center, 3251 Hanover Street, Palo Alto, CA 94304, USA
Alfred Krabbe Deutsche SOFIA Institut, University of Stuttgart, 70569
Stuttgart, Germany  Robert Minchin National Radio Astronomy Observatory, P.O.
Box O, Socorro, NM 87801, USA  Albrecht Poglitsch Max Planck Institute for
Extraterrestrial Physics, 85748 Garching, Germany

(Received 06/30/2023; Revised 09/29/2023; Accepted 10/02/2023)

###### Abstract

We present the characterization and definitive flux calibration of the Far-
Infrared Field Integral Line Spectrometer (FIFI-LS) instrument on-board SOFIA.
The work is based on measurements made in the laboratory with an internal
calibrator and on observations of planets, moons, and asteroids as absolute
flux calibrators made during the entire lifetime of the instrument. We
describe the techniques used to derive flat-fields, water vapor column
estimates, detector linearity, spectral and spatial resolutions, and absolute
flux calibration. Two sets of responses are presented, before and after the
entrance filter window was changed in 2018 to improve the sensitivity at
52$\mu$m, a wavelength range previously not covered by PACS on Herschel. The
relative spectral response of each detector and the illumination pattern of
the arrays of the FIFI-LS arrays are derived using the internal calibrator
before each observational series. The linearity of the array response is
estimated by considering observations of bright sources. We find that the
deviation from linearity of the FIFI-LS arrays affects the flux estimations
less than 1%. The flux calibration accuracy is estimated to be 15% or better
across the entire wavelength range of the instrument. The limited availability
of sky calibrators during each observational series is the major limiting
factor of the flux calibration accuracy.

Far infrared astronomy(529) – Astronomical instrumentation (799) – Flux
calibration(544)

††journal: AJ††facilities: SOFIA(FIFI-LS), Herschel(PACS)††software:  astropy
(Astropy Collaboration et al., 2013), sospex (Fadda & Chambers, 2018), HIPE
(Ott, 2010), pyfifi (Vacca et al., 2020)

##  1 Introduction

FIFI-LS (Colditz et al., 2018; Fischer et al., 2018) was the far-infrared
field integral line spectrometer for SOFIA (Krabbe, 2000) and performed field
spectroscopy in the wavelength range 50$\mu$m - 200$\mu$m. The instrument was
originally developed at the Max Planck Institute in Garching (Germany, P.I.:
A. Poglitsch) in parallel with the PACS instrument (Poglitsch et al., 2010)
and offered as a facility instrument to SOFIA (Klein et al., 2010). In 2012,
the development was transferred to the University of Stuttgart under a new
P.I. (A. Krabbe). FIFI-LS was commissioned in 2014 (Klein et al., 2014) and
used for science observations thereafter. In the last few years the instrument
was improved by activating the internal calibrator for laboratory measurements
(2017) and changing the entrance filter window to improve its sensitivity at
52$\mu$m (2018), a wavelength regime that was not accessible to the PACS
instrument on Herschel. The last observations with FIFI-LS were made in
September 2022, the month when the SOFIA observatory was decommissioned by
NASA.

Figure 1: Sky position and size of each spatial pixel (spaxel) for the blue
and red array. The plot axes denote the offset in arcseconds from the center
of the red array (spaxel 13). The blue and red fields of view are shifted by
approximately 6 arcsec in the horizontal direction of the array. The numbers
correspond to the way the image was sliced. The rows (1-5, 6-10, and so on)
were rearranged into pseudo-slits which were dispersed by gratings onto the
blue and red detectors.

In this paper, we present the characterization of the spatial and spectral
resolution of FIFI-LS and study the response of the detectors. Several
measurements have been done in the laboratory using the internal calibrator.
However, due to poor knowledge of the calibrator emission, the absolute
calibration was carried out via observations of celestial calibrators such as
asteroids, moons, and planets, as it was the case for PACS. The techniques
used to analyze these data, especially to correct them for the effects of the
atmosphere, are discussed here. Several objects observed with PACS on Herschel
were re-observed with FIFI-LS providing us with the possibility of cross-
correlating the flux calibrations of the two instruments. We present the
definitive absolute flux calibration for FIFI-LS, computed for the two epochs
of the instrument, as defined by the change of the access filter window in
2018, as well as updated estimates of instrumental sensitivity, spectral, and
spatial resolution with respect to those presented in previous publications
(Colditz et al., 2018; Fischer et al., 2018). To guide FIFI-LS data users and
allow comparisons between recent and previously published results, the
differences with the previous calibration release are discussed in detail in
the section about the absolute flux calibration.

##  2 Data

###  2.1 Detectors

FIFI-LS was an integral field spectrograph able to simultaneously obtain
spectra in two different spectral channels over a square field-of-view. To
account for the increasing width of the point spread functions (PSF) as a
function of wavelength, the blue and red arrays had different pixel sizes and
consequently different fields of view. We will refer in the following to
pixels in the sky as spaxels, short for spatial pixels. The spaxels are
approximately square with a size on the sky of 12.2$\times$12.5 sq. arcsec and
6.14$\times$6.25 sq. arcsec for the red and blue arrays, respectively. As
shown in Figure 1, the field of view of the two arrays were also slightly
shifted with respect to each other by approximately 6 arcseconds in the
horizontal direction. By using the spaxel numbering shown in Fig. 1, when the
target is centered on the red array (spaxel 13), it falls on the spaxel 12 in
the blue array. The spaxels were not perfectly arranged in a grid because of
the complexity of aligning the mirrors in each of the integral field units.
Moreover, the spaxels of the last column (# 5, 10, 15, 20, and 25) which are
shown in Fig. 1 as partially overlapping the adjacent spaxels, are only
partially illuminated and require the largest flat correction (see Sec. 3.3).

As elegantly described in Looney et al. (2003), the light was first split into
two bands by a dichroic, then sliced into 5 different slices which were
rearranged along a one-dimensional pseudo-slit by a system of mirrors. This
pseudo-slit comprised the 25 spaxels and served as the entrance for the
grating spectrometer. Two different dichroics were used in order to split the
light at 105 and 130$\mu$m. The dichroics allowed one to simultaneously
observe two different lines for the same object, since the red and blue arrays
each had its own independent grating. Using each of the dichroics, a line in
the overlapping region 105-130$\mu$m could be observed either with red or the
blue array. Separate blue and red gratings then dispersed the light from each
of the pseudo-slit spaxels across 18 spectral pixels. Therefore, the detector
arrays consisted of 18 spectral by 25 spatial pixels. However, the two ends of
each spectral pixel row were (by design) not illuminated by the sky. In
particular the first one was open and can be considered as a bias pixel in a
normal optical CCD, while the last one was a resistor pixel which has an
additional signal. The open pixel can be used in the data reduction to remove
correlated noise, which increases the noise in the ramps (see Sec. 3.8.1).
Thus a total of 16 $\times$ 25 pixels were illuminated by the sky.

###  2.2 Ramps

Several observing modes were used by FIFI-LS. The most commonly used was the
so-called symmetric chop-nod mode. To remove the background emission, the
secondary mirror was tilted to target alternatively between the source and a
sky position (chopped) and the flux of the two beam positions subtracted.
However, since the two positions saw a different part of the primary mirror
and had slightly different optical paths, the telescope was periodically moved
(nodded) to swap the two beams in order to have the target in the other beam
position (in what used to be the sky beam), and remove this residual effect by
averaging the two measurements. This is the technique used to obtain all of
the calibration data discussed in this paper.

Figure 2:  Left: group of 4 ramps (2 on- and 2 off-target) during an
observation of Mars. Right: Slope between consecutive readouts for the on- and
off-target ramps. The median for each readout is marked with a darker color.
The difference in the average slope between the on- and off-target
observations is due to the Mars flux over the dominant background flux. The
first and last readouts are discarded in the analysis.

The charges on the detectors were sampled with a series of non-destructive
readouts followed by a reset. Since at each readout the charges on the
detector increase, this is usually referred as a ramp and the incident flux
can be derived as the slope of the ramp (slope of the charge versus time), an
approach called up-the-ramp fitting. In particular, a ramp consisted of 32
readouts taken in 1/8 s. The minimal integration consisted of two ramps in one
chop position and other two in the second chop position for a total of 0.5 s,
i.e. a chop frequency of 2 Hz. During the last readout the telescope moved to
the next chop position, so this readout is usually discarded. The first
readout after the detector reset is highly non-linear and it is also
discarded. The linearity and saturation of ramps of the different pixels is
discussed in section 3.2. Each set of four ramps was repeated several times,
depending on the integration time requested. Then, the chop positions were
inverted for the next nod observation. Part of one observation of Mars is
shown in Fig. 2. The left panel shows a group of four ramps which constitutes
a minimal observation composed of 2 on- and 2 off-ramps. The right panel shows
the slopes between consecutive readouts for all the ramps relative to a
grating position. This clearly shows that the first readout has to be
discarded, as well as the last one which is affected by the chopper movement.
The difference in flux (measured in the slope V/s) of the two groups of ramps
is due to the flux of Mars on the detector for the on-ramps, while the off-
ramps only register background flux. Even in the case of a strong source such
as Mars, the signal is dominated by the background due to emission from the
sky and telescope. In this specific case, Mars contributes less than 3% to the
total signal.

The ramps are stored in FITS files as signed integers. To convert the ramp
values into Volts, the following formula should be used:

$r[V]=\frac{r+2^{15}}{2^{16}}3.63\,V,$ (1)

where $r$ is the value of the ramp stored in the FITS files of the
observation. The FIFI-LS pipeline (Vacca et al., 2020) does not implement this
conversion and computes directly the slope of the data from the instrumental
units. We call ADU (analog-digital units) the units of the slope as computed
by the pipeline. Then, to obtain a flux density, the slope is divided by the
width of the frequency channel corresponding to a single pixel to obtain
values in ADU/Hz. For this reason, we express the response in terms of ADU
Hz-1 Jy-1.

###  2.3 Change of filter window

In 2018 the entrance filter window was changed in order to improve the
sensitivity of FIFI-LS at 52$\mu$m to observe the line of [OIII]51.81$\mu$m
which was not observable with PACS on Herschel. The change was successful and
allowed for important observations to estimate the metallicity in galaxies
with far-infrared lines (see, e.g., Chen et al., 2023; Chartab et al., 2022).
Since this change affected the responses for the two arrays and orders, we
present two sets of responses for each combination of array/order/dichroic.
The last flight with the old entrance window is Flight 424 in flight series
OC5I, while the second set of responses are valid starting from Flight 524 in
OC6M.

###  2.4 Pre-flight calibration

SOFIA was able to observe with only one instrument at a time mounted on the
telescope. For this reason, FIFI-LS was mounted and used for a series of
flights which we define as an observational flight series. Before being
mounted on the telescope, the FIFI-LS instrument was inspected, vacuum pumped,
and cooled down. For each cooldown of the instrument, several calibration
measurements were needed since tiny mechanical changes resulted in slightly
modified optical paths. In particular, three series of measurements were
performed: (i) wavelength calibration, (ii) alignment of the beam rotator
(K-mirror) (Colditz et al., 2014), and (iii) flats.

The wavelength calibration was performed by observing several water vapor
lines with gas cells at different pressures. The procedure used is detailed in
Colditz et al. (2018). After the change of the filter window, observations of
two additional lines at 47.9732 and 51.0711 $\mu$m were added to the procedure
to improve the calibration at the 2nd order blue end. These two lines are
sufficiently narrow to appear as unresolved lines even when using water vapor
in the gas cell. For this reason, these lines have also been used in the study
of the spectral resolution of FIFI-LS (see Sec. 3.4).

The first part of the calibration of the beam rotator – called K-mirror
because it is composed of 3 mirrors combined in a way which resembles the
letter K – was done following the technique detailed in Colditz et al. (2014).
The measurement of the rotation vector, i.e. the vector connecting the center
of rotation to the center of the array, was done using the telescope
simulator, a system mounted to the instrument in the laboratory which was able
to simulate a point source. The position of the point source was measured at
different angles of rotation of the image to infer the parameters of the
rotation vector.

Finally, several spectral scans with the internal calibrator at 150 K were
done by covering all the bands (red, blue 1st order and 2nd order) with the
two dichroics in order to compute the relative response of the detectors. The
computation of the flats is described at length in Section 3.3.

###  2.5 In-flight calibration

During each observational series several observations were dedicated to
calibrate the instrument.

At the beginning of each series, the rotational parameters of the K-mirror
obtained in the laboratory were verified by repeating the measurements of a
point source when rotating the beam. An accurate knowledge of the rotational
parameters was essential since the K-mirror was used not only to orient the
field at a certain angle, but also to counteract the rotation of the sky
during the so-called rewinds of the telescope. In fact, although the telescope
was alt-azimuth mounted, it tracked inertially following the sky like an
equatorial mounted telescope rotating around its line-of-sight axis. However,
the amount it could rotate about the cross-elevation (i.e., “azimuth”) and
line-of-sight (i.e., “position angle”) axes was limited between $\pm 2.8^{o}$.
When the telescope reached its limit in line-of-sight rotation, it was rotated
back. This rewind was counteracted by a rotation of the K-mirror to keep the
position angle of the array on the sky fixed. Such a rotation, since the
K-mirror was not perfectly aligned, introduced a small boresight change which
was compensated by the telescope.

In between flight legs, which usually corresponded to different targets, the
initial minutes were devoted to observe a few telluric lines to estimate the
zenith precipitable water vapor. The procedure employed for these measurements
is discussed in Section 3.6.

In each series we observed several calibrators to estimate the absolute flux
calibration. The best data were obtained by observing Mars, the brightest
source small enough to fit within the FIFI-LS detector footprint. However,
Mars was not available during all flight series and secondary calibrators were
used (Neptune, the Galilean moons, and asteroids). These calibrators were
observed in all the array/order/dichroic combinations covering the whole
spectral range. The analysis of the flux calibration is presented in Section
3.7.

Finally, we observed point-source calibrators at a few key-wavelengths to have
a direct measurement of the spatial point spread function of FIFI-LS. The
results of this analysis are presented in Section 3.5.

##  3 Analysis

Figure 3:  Percentage of bad pixels in the two arrays as a function of the
date of the observational series.

###  3.1 Bad pixels

A few pixels of the two detectors with very low responsivity are masked by the
FIFI-LS pipeline. The lists of these pixels were compiled before each
observational series by inspecting the laboratory calibration data. Figure 3
shows the percentage of bad pixels as a function of the array and date. The
percentage of bad pixels for the blue array is around 5%, while for the red
array is slightly higher (8%). The number of bad pixels slowly increased with
time, although some pixels not responding in one series could work again after
a cooling cycle in a subsequent series.

In 2021 all of the pixels corresponding to the spaxels #3 and #21 of the red
array became unresponsive. Later in 2022, spaxel #10 became unresponsive. The
cold readout electronics for these spaxels were identified as the most likely
cause of the issue. A new electronic board was prepared and the repair was
scheduled in 2022. However, because of the abrupt end of the SOFIA mission, it
was decided to observe as much as possible with FIFI-LS before the
decommissioning date and this prevented the upgrade of the electronics.

Figure 4: Top: Linearization of ramps for a pixel in the red array. Middle:
linearization coefficient $\alpha$ versus saturation level for all the pixels
in the red array. For most of the pixels $\alpha$ is around -0.03.

Bottom: percentual correction of ramp slopes after linearization for the red
array for an entire Mars observation. The median correction is marked with a
cyan line.

###  3.2 Linearity

In an ideal detector the relationship between the incident flux and the
measured voltage is linear along a ramp. A real detector, however, has a
linear behavior only in a limited flux range. Beyond a certain flux it becomes
non-linear until saturation when it reaches the maximum amount of charge that
it can collect, and the measured voltage no longer relates to the incident
flux.

Figure 5:  Flux measured for each pixel of the blue and red arrays (using the
dichroic 105 $\mu$m), after scaling each pixel flux to the median value of
their spaxel. This data was taken in March 2018, before an observational
series. To make them visible, the fluxes from the different spaxels are spaced
by $0.5\,10^{-10}$ and $10^{-10}$ ADU/Hz in the case of the blue and red
arrays, respectively. While the different pixels in one spaxel detect a very
similar flux in the blue array, the red array is less uniform, especially in
the reddest part of the spectrum.

To estimate the linearity of the FIFI-LS detectors we considered a quadratic
term in the ramps as a first approximation to the observed ramps. By assuming
a single non-linearity term, we can in principle linearize the ramps once the
coefficient of non-linearity is known. Let us assume then, as done in the
Spitzer IRS
handbook111https://irsa.ipac.caltech.edu/data/SPITZER/docs/irs/irsinstrumenthandbook/41/,
that the observed signal can be written as the sum of the ideal linear signal
and a quadratic term that takes into account the non-linearity of the
detector:

$S_{obs}=S_{lin}+\alpha S_{lin}^{2},$ (2)

where $\alpha$ is the non-linearity coefficient. Once $\alpha$ is estimated
for each pixel, the equation can be easily inverted to linearize the ramps:

$S_{lin}=\frac{2S_{obs}}{1+\sqrt{1+4\alpha S_{obs}}}.$ (3)

The top panel of Fig. 4 shows the technique used to estimate the optimal value
of the quadratic term $\alpha$ for a particular pixel. The slopes between
consecutive readouts for several ramps of a pixel observing the same object
are plotted in blue. A linear behavior would result in a constant value for
the slope between consecutive ramps. The example shows that, as charges
accumulate on the detector, the slope between readouts changes revealing a
non-linear behavior. By computing the slope of the ramps one obtains a value
marked with a blue line which is lower than the actual flux. To evaluate the
optimal $\alpha$ needed for the linearity correction, we computed the
$\chi^{2}$ of the residuals of the corrected slope from the median value of
the consecutive slopes. The optimal value with the minimum $\chi^{2}$ shown in
the inset gives the best correction. The slopes of the corrected ramps are
shown with orange dots and are now in much better agreement with the slope
computed from the entire ramp (orange line). In the computation the first and
last slope are discarded since they are affected by the reset and chop change.

Figure 6:  Left: Spatial flats color coded by observational series. The
partially illuminated column (spaxels 5,10,15,20, and 25) has usually lower
and more dispersed values than those of other spaxels. The effect is
particularly evident in the blue channel. Right: Spectral flats for all the
spaxels of the red array, dichroic 105$\mu$m, pixel # 6. The blue lines
correspond to the measurements from all the FIFI-LS series after applying the
spatial flats of each series. The black lines are the accepted flats computed
via a Chebyshev polynomial smoothing.

The middle panel in Fig. 4 shows the values for the linearity correction
coefficient $\alpha$ and the saturation level of the ramp for each pixel in
the red array. Similar results are obtained for the blue array. Ramps saturate
with voltages greater than 2.4 V., while $\alpha$ is typically around -0.03
except for a few pixels with higher saturation values.

Finally, the bottom panel of Fig. 4 shows the effect of linearizing the ramps
on the estimate of their slopes in the case of the red array. The comparison
is between all the observations of Mars with the red array done during Flight
312. There is a systematic effect corresponding to less than 3% of the slope.
However, the dispersion is less than 1% for slopes higher than 0.1 mV/s. Since
the systematic effect is absorbed by the flux calibration (which will be also
systematically lower), the effect of the linearization of the ramps is in
general around 1%. For this reason, the linearization of the ramps has not
been introduced in the FIFI-LS pipeline.

###  3.3 Flats

Spectral scans of the internal calibrator were used to estimate the flats in
the different arrays, orders, and dichroics. The internal calibrator was
heated at 150 K to have a signal close to the background radiation observed in
flight. These measurements were repeated before each flight series to take
into account the effect of small mechanical changes in the instruments
produced by different cool downs.

The biggest effect of these changes was the variation in illumination of the
array. Slight differences in the optical path produced changes in the
illumination patterns. To estimate such variations, we considered the median
flux detected in all the pixels relative to the same spaxel and computed the
ratio of such values to the median flux of all the spaxels. Figure 5 shows the
curves measured in March 2018 using the dichroic splitting the light at 105
$\mu$m. For each spaxel, the curves of the 16 pixels have been normalized to a
median value. In the blue array (two orders in the left side part of the
figure) the different pixels have a very similar response. The situation is
different for the red array, where the curves differ much more, especially at
the longest wavelengths. This behavior can be explained by taking into account
the fact that the detector elements in the red array are compressed in their
mounting structures in order to shift the area of good spectral sensitivity
into the wavelength range of 120–210$\mu$m (Rosenthal et al., 2000). Since the
pressure applied is not perfectly even, the shape of the response curves of
the different pixels varies more than those of the blue array and this is more
pronounced at the far-IR end where the detector sensitivity is the lowest.

Figure 7:  Top:  from left to right, examples of line profiles in the blue 2nd
order, blue 1st order, and red. The residuals from fits with different
functions are shown on the bottom. In general lines are a little asymmetric,
especially in the blue. Bottom:  Spectral resolution for the three bands of
FIFI-LS: blue in two diffraction orders and the red array.

The spatial flats were derived from the ratio of the median spaxel curves in
Figure 5 to the median global curve for each observational series. The spatial
flats for the two arrays are plotted on the left panel of Fig. 6. The spaxels
relative to one of the lateral columns (5,10,15,20, and 25) usually have the
lowest fluxes and the biggest dispersions between observational series. These
spaxels were in fact partially illuminated. For this reason, we did not
consider them when obtaining the median signal from the various pixels and
when obtaining the response curve in Section 3.7.3.

Finally, to obtain the spectral flat of each pixel, we normalized the data
from each series with the aforementioned spatial flat field and coadded the
ratios of the pixel curves to the median curve of the entire array. As an
example, in Fig. 6 the curves from different series for the pixel 6 of the red
array are shown in blue. The spectral flat, computed as a mean behavior by
using Chebyshev polynomials, is shown with a black line.

###  3.4 Line Profile and Spectral Resolution

Several lines have been measured in the laboratory before each observational
run with the purpose of calibrating the instrument in wavelength. To have a
high signal-to-noise signal, these measurements were done with ‘pure H2O’ at a
pressure of 5 mBar. However, some of these lines are broader than the spectral
resolution of FIFI-LS. To better study their profile and the spectral
resolution at different wavelengths, a few lines have been also observed with
’air’ cells which have air at the pressure of 10 mBar. The list of the lines
used is reported in Colditz et al. (2018) with the exception of two new lines
(47.9732 and 51.0711 $\mu$m) which were added in 2018 when the filter window
was changed to extend the range of FIFI-LS down to 47$\mu$m.

To study the profile of the lines, we tried to fit the lines with several
functions: Gaussian, Voigt, pseudo-Voigt, and asymmetric functions such as a
skewed Gaussian, a skewed Voigt, and an asymmetric pseudo-Voigt. For all these
functions we used the implementation in the Python package lmfit
222https://lmfit.github.io/lmfit-py/builtin_models.html with the exception of
the asymmetric pseudo-Voigt for which we followed the article where it was
proposed (Stankic & Brouns, 2008).

The pseudo-Voigt profile is a very good approximation of the Voigt profile
obtained as a sum of fractional contributions of the Gaussian and Lorentzian
profiles:

$PV(\lambda)=f\,G(\lambda)+(1-f)\,L(\lambda),$ (4)

with $f$ between 0 and 1. By modifying the dispersion as a function of the
distance from the center of the line:

$\sigma_{a}=\frac{2\sigma}{1+e^{a(\lambda-\lambda_{0})}},$ (5)

with $a$ parameter of asymmetry and $\lambda_{0}$ center of the line, one
obtains the asymmetric pseudo-Voigt profile.

In general lines in the blue 2nd order are slightly asymmetric. Although the
best fits are obtained with a skewed Gaussian or an asymmetric pseudo-Voigt, a
pseudo-Voigt is still a good approximation. The case of the 1st order in the
blue is different. As already remarked by Colditz et al. (2018) (see Fig. 3),
the profile of the line changes in different pixels. The combination of all
the pixel signals in Fig. 7 results in an asymmetric profile with a bump on
the higher wavelength side. The best shapes to reproduce this unusual profile
are either the skewed Gaussian or the asymmetric pseudo-Voigt. Finally, the
profile of the lines in the red array are much more regular. They can be
fitted very well with a simple pseudo-Voigt. The profile is well behaved and
has the smallest residuals among the different bands.

To measure the full-width half-maximum (FWHM) of the lines, we smoothed the
combination of all the measurements normalized to 1 as shown in the top panel
of Fig. 7 with the non-parametric fitting technique called LOWESS which is
available in the statsmodel library in Python. Then, we directly measured the
width at 0.5.

Figure 8: Measurements of the FWHM of the spatial PSF at several key
wavelenghts. The values are higher than the diffraction limit of the telescope
(solid grey line) because of a small instrumental contribution (dashed line).
However, the instrumental part dominates in the 2nd order of the blue array.

The bottom panel of Fig. 7 shows the FWHM measured values with lines at
different wavelengths. The red points are done using water vapor cells, while
the blue points correspond to measurements with ambient air cells. Pure water
vapor gives a stronger emission but also a wider FWHM. For this reason, lines
with a FWHM close to the spectral resolution have been observed with air
cells.

In the fit to obtain a relationship for the spectral resolution, we did not
consider lines measured with H2O cells which are broader than the spectral
resolution. The plot reports some of these measurements from different series
to show their spread due to the H2O amount in the cell being variable. They
are represented as lower limits with an arrow pointed upwards instead of an
error bar.

The reported values are median values of the measurements in all the spaxels,
while the dispersion values correspond to the dispersion of the values in the
different spaxels. A polynomial has been fitted to the points to obtain the
dependency of the resolution on the wavelength. A second-degree polynomial is
used for the blue array while, in the case of the red array, a first-degree
polynomial is sufficient to fit the relationship.

$\displaystyle R$ $\displaystyle=$ $\displaystyle 11.14\lambda-550.28$ red
$\displaystyle R$ $\displaystyle=$ $\displaystyle
0.1934\lambda^{2}-28.89\lambda+1664$ blue 1st ord (6) $\displaystyle R$
$\displaystyle=$ $\displaystyle 1.937\lambda^{2}-113.7\lambda+2932$ blue 2nd
ord

Table 1: Measurements of spatial resolution Source | Flight | Band | Wavelength | FWHM
---|---|---|---|---
name | number |  | [$\mu$m] | [arcsec]
Uranus | 636 | B2 | 52.0 | 7.1 $\pm$ 0.8
Uranus | 636 | R | 158.5 | 15.3 $\pm$ 2.2
Uranus | 665 | B2 | 62.1 | 7.5 $\pm$ 0.9
Uranus | 665 | B1 | 88.35 | 8.8 $\pm$ 1.0
Uranus | 665 | R | 145.45 | 14.2 $\pm$ 3.4
Uranus | 665 | R | 185.85 | 17.6 $\pm$ 4.7
Callisto | 680 | R | 129.8 | 13.0 $\pm$ 0.2
Callisto | 680 | R | 142.3 | 13.9 $\pm$ 0.8
Callisto | 680 | R | 171.5 | 16.1 $\pm$ 1.3
IRC+10216 | 737 | R | 157.7 | 15.2 $\pm$ 1.4
Ganymede | 738 | B2 | 69.3 | 7.5$\pm$ 0.7
Ganymede | 738 | R | 130.1 | 13.6$\pm$1.6
Europa | 740 | B1 | 97.1 | 9.5$\pm$0.9
Ceres | 806 | B1 | 102.6 | 9.8$\pm$0.7
Ceres | 806 | B1 | 110.5 | 10.7$\pm$0.7
Ceres | 806 | R | 142.2 | 13.8$\pm$1.4
Ceres | 806 | R | 150.1 | 13.7$\pm$1.9

###  3.5 Spatial Resolution

As shown in Colditz et al. (2018) (Figure 11), the instrumental point spread
function (PSF) has a FWHM usually smaller than the diffraction limit of the
telescope, with the exception of the second order in the blue where it is
bigger. To better study the instrumental effects on the size of PSF, we
observed several point sources at different key wavelengths in the red array
and the two orders of the blue array. For such observations we used a fine
dithering pattern in order to better recover the shape of the PSF. We then
fitted a Moffat function (Moffat, 1969) to the distribution of the fluxes as a
function of the distance from the center of the target. Table 1 reports the
objects and measurements considered to obtain the spatial resolution of FIFI-
LS as a function of the wavelength. These values are plotted in Figure 8 with
overplotted the diffraction limit of the telescope (as a continuous grey
line), the instrumental contribution to the PSF, and the real FWHM obtaining
by combining quadratically these two components. The diffraction limit is
computed using the formula of the point spread function for obstructed mirrors
(Born & Wolf, 1970):

$I[u]=\frac{1}{(1-\epsilon^{2})^{2}}\left[\frac{2J_{1}(u)}{u}-\epsilon^{2}\frac{2J_{1}(\epsilon
u)}{\epsilon u}\right]^{2}$ (7)

with $u=\frac{\pi}{\lambda}D\theta$, $D$ diameter of the mirror, and
$\epsilon$ the fractional radius of the central obscuration of the primary
aperture. Since the entrance pupil diameter is 2.5 m and the aperture stop
diameter is 0.352 m, the obstruction factor is $\epsilon=0.352/2.5=0.14$
(Krabbe, 2000). Finally, $J_{1}$ corresponds to a Bessel function of the first
kind. The FWHM corresponds to the distance at which $I[u]$ drops to half of
the central value, which leads to the theoretical diffraction limit of:

$FWHM[rad]=1.018\cdot 10^{-6}\cdot\frac{\lambda[\mu m]}{D[m]},$ (8)

a value smaller than that of an unobstructed mirror.

To compute the instrumental contributions, we considered the geometric mean of
the parameters in Table 3 of Colditz et al. (2018) in the two dimensions
(along and perpendicular to the slits) and we used the conversion factor 3.55
from mm to arcsec on the sky estimated for the telescope simulator. We then
shifted the values by subtracting 2.6, 0.8, and 5.0 arcsec for the blue 2nd
order, 1st order, and red arrays, respectively, to better fit the measured
points. We remind that the parameters for the instrumental PSF were obtained
with a simulated source which was not perfectly point-like, so the
instrumental contribution was overestimated.

Finally, for reference, we overplotted the diffraction limit for an
unobstructed mirror of the same size of the SOFIA telescope, with a dotted
line, using the standard formula $1.22\lambda/D$, with $D$ the diameter of the
telescope mirror. We can see that, except for wavelengths shorter than
70$\mu$m, this is a good approximation of the FWHM of the FIFI-LS point spread
function. Simple linear relationships can be used to estimate the FIFI-LS
spatial resolution at different wavelengths:

$\displaystyle FWHM[arcsec]$ $\displaystyle=$ $\displaystyle
0.097\cdot\lambda[\mu m]$ red, blue 1st $\displaystyle=$ $\displaystyle
3+0.07\cdot\lambda[\mu m]$ blue 2nd (9)

###  3.6 Precipitable water vapor

Although flying over more than 99% of the water vapor in the atmosphere, the
SOFIA observatory was still affected by the presence of the atmosphere. An
important part of the data reduction consists in selecting the best
atmospheric model to correct for atmospheric transmission and telluric
absorptions. The most prominent telluric absorptions are due to water vapor.
For this reason, the main parameters considered in atmospheric models are the
altitude of the observation, the elevation angle of the telescope, and the
water vapor present in the atmosphere. The two first quantities are known,
while the zenith precipitable water vapor (PWV) has to be measured. A water
vapor monitor was developed for SOFIA to continuously measure the zenithal PWV
(Roellig et al., 2010). Unfortunately, the implementation of this instrument
has been problematic and its measurements were extremely unreliable. For this
reason, the FIFI-LS team devised a technique to monitor the water vapor values
in between the flight legs. As described in Fischer et al. (2021), a short
spectroscopic scan was performed to observe a few strong water vapor telluric
features in the blue and red array several times during a flight. These
features were then fitted with a grid of ATRAN models (Lord, 1992) with
different values of precipitable water vapor in order to select the value
minimizing the residuals (see top panel of Figure 9).

Figure 9: Top: telluric features used for estimating the zenith precipitable
water vapor (PWV). The left panel shows the value of water vapor at the zenith
(WVZ) which minimizes the residuals between model and data. The corresponding
model is shown in the right panels plotted in yellow over the features
observed with the blue and red arrays. Middle: satellite values scaled to the
observed PWV values for one the last flights of FIFI-LS (flight 907). The data
at the beginning of the flight, when the telescope is still cooling down, is
discarded when computing the scaling factor. Bottom: Precipitable water vapor
values (PWV) as a function of altitude and season (October to March in green,
and April to September in orange) for the flights in the Northern hemisphere.

Then, following the procedure outlined by Iserlohe et al. (2021), the values
from the ERA5 model (Hersbach et al., 2020) based on satellite observations
were scaled to the values measured in flight to estimate the zenith PWV at
each instant of the flight (see Figure 9, middle panel). Figure 9 shows the
importance of having an estimate of the water vapor during the entire flight.
In fact, the values between the second and fourth hour of the flight vary by
more than 5$\mu$m, while the sample measurements show some variation but
cannot quantify it in an accurate way. Also, the variation between the fifth
and sixth hour of the flight would have been completely unnoticed. The
availability of satellite data, scaled to the direct measurements in flight,
allows one to accurately reconstruct the variation of the water vapor along
the entire observation. The scaling factors found in the different flights
vary between 0.55 and 0.65, with a median value of 0.6. This is the scaling
factor adopted for all the flights before flight 524, the first flight for
which PWV measurements were performed. Iserlohe et al. (2022) extended the
comparison between the FIFI-LS measurements and another re-analysis of
atmospheric satellite data (MERRA-2) finding a linear relationship with
different scale factors than those with the ERA5 data. The dispersion of the
relationship is however worse than that with the ERA5 data. Zenithal PWV
values are saved in the header of the raw archived files for each FIFI-LS
observation and can be read and used by the FIFI-LS pipeline. When reducing
data taken before flight 524, it is advisable to experiment with rescaling the
water vapor measurements in the header to better remove the residuals of
telluric absorption.

The bottom panel of Fig. 9 shows the distributions of the zenith PWV values
measured in all the flights in the Northern Hemisphere as a function of the
barometric altitude. The plot is divided according to the period of
observation, since the altitude of the troposphere depends on the temperature
and therefore flying at the same barometric altitude corresponds to a
different precipitable water vapor. In particular, we split the year into a
summer season (between April and September) and a winter season (between
October and March). It is evident that the values in the warm months have a
larger spread in values and a higher median at any altitude than those in the
cold months of the year. While during cold months good conditions are reached
at 39-40,000 feet, one has to reach the altitude of 42,000 feet to have good
values of water vapor in the summer. It is not possible to make an analog
study for the Southern Hemisphere since we only collected usable water vapor
data during seven flights in Chile.

###  3.7 Flux calibration

As discussed in Section 3.3, FIFI-LS has an internal calibrator.
Theoretically, if the internal grey body spectral distribution were known and
were stable, it would have been possible to compute the absolute calibration
factor directly in the laboratory. Since these two conditions were not met, we
used sky calibrators to derive the absolute calibration. The observations
consisted in spectral scans of a calibrator in any order and choice of
dichroic, centering the target on the first four columns of the detectors (see
Figure 1) to avoid the partially illuminated column. This strategy also
minimized the effect of the spatial ghost, described in Section 3.3 of Colditz
et al. (2018). The technique was perfected only in 2015. Before this date only
very small parts of the spectral energy distribution of sky calibrators were
observed. These old observations are not used in the current work since it is
difficult to remove flat residuals and do a satisfying atmospheric correction
in such short scans. The total flux of the calibrator is then computed by
adding the flux from all the spaxels with the exception of the partially
illuminated column which was also affected by the ghost source.

####  3.7.1 Calibrators

Several sky calibrators were observed during the lifetime of FIFI-LS. The
primary calibrator was Mars since it is very bright at any wavelength observed
with FIFI-LS. Although it does not appear to be a point source during certain
periods of the year, it is sufficiently point-like to be completely covered by
the FIFI-LS blue and red arrays. Secondary calibrators used were Uranus,
Jovian moons, and bright asteroids. In the present work we used them only when
absolutely necessary, since the signal from these sources is very faint. In
particular, we did not use them to define the response of the red array. The
models used for the absolute flux of Mars are those developed for Herschel by
Lellouch and Moreno 333http://www.lesia.obspm.fr/perso/emmanuel-
lellouch/mars/. Model fluxes were computed at a number of discrete
wavelengths, and these were fitted with a blackbody to provide fluxes at all
wavelengths across the entire wavelength range of FIFI-LS. In the case of
Uranus we used the ESA2 model developed by Orton et al. (2014), which was also
used for the calibration of PACS on Herschel. For the Jovian moons, we used
the ESA2 models developed for Herschel by Moreno (see Müller et al., 2016).
All these models are distributed with the SOFIA pipelines
444https://github.com/SOFIA-
USRA/sofia_redux/tree/main/sofia_redux/calibration/data/models. The list of
the objects used to obtain the absolute calibration of FIFI-LS is reported in
Table 2.

Table 2: List of flux calibrators Date | Flight | Source | Band | Range [$\mu$m] | Scaling | Date | Flight | Source | Band | Range [$\mu$m] | Scaling
---|---|---|---|---|---|---|---|---|---|---|---
2015 Oct 22 | 249 | Mars | B1-105 | 76-96 | 0.90 | 2019 Feb 27 | 548 | Mars | R-105 | 115-168 | 0.99
2015 Oct 22 | 249 | Mars | R-105 | 126-156 | 0.95 | 2019 Feb 27 | 548 | Mars | R-130 | 145-190 | 1.01
2016 Feb 27 | 281 | Mars | B2-105 | 59-75 | 1.03 | 2019 Feb 28 | 549 | Mars | B1-105 | 65-105 | 1.00
2016 Mar 01 | 282 | Mars | B2-105 | 51-61 | 1.00 | 2019 Feb 28 | 549 | Mars | B2-130 | 49-55 | 1.00
2016 Mar 01 | 282 | Mars | B1-130 | 86-104 | 1.04 | 2019 Feb 28 | 549 | Mars | R-105 | 155-205 | 1.01
2016 Mar 01 | 282 | Mars | R-105 | 118-148 | 1.01 | 2019 Feb 28 | 549 | Mars | R-130 | 120-131 | 1.00
2016 Mar 01 | 282 | Mars | R-130 | 169-188 | 1.00 | 2019 May 02 | 563 | Mars | B2-105 | 50-60 | 0.97
2016 Mar 09 | 286 | Mars | B1-105 | 74-96 | 0.99 | 2019 May 02 | 563 | Mars | B2-130 | 50-65 | 1.04
2016 Mar 09 | 286 | Mars | R-105 | 124-158 | 1.00 | 2019 May 02 | 563 | Mars | R-105 | 185-205 | 0.82
2016 Jun 30 | 312 | Mars | B2-105 | 51-70 | 0.99 | 2019 May 02 | 563 | Mars | R-130 | 181-205 | 0.89
2016 Jun 30 | 312 | Mars | R-105 | 118-175 | 1.11 | 2021 Apr 13 | 716 | Mars | B2-105 | 50-60 | 1.06
2016 Jul 03 | 314 | Mars | B1-105 | 71-118 | 0.97 | 2021 Apr 13 | 716 | Mars | R-105 | 115-148 | 0.96
2016 Jul 03 | 314 | Mars | R-105 | 163-201 | 0.96 | 2021 Apr 14 | 717 | Mars | B1-105 | 67-87 | 1.05
2016 Jul 05 | 316 | Mars | B1-130 | 114-125 | 0.92 | 2021 Apr 14 | 717 | Mars | B2-130 | 50-70 | 0.97
2016 Jul 05 | 316 | Mars | R-105 | 198-205 | 0.95 | 2021 Apr 14 | 717 | Mars | R-105 | 156-178 | 1.00
2016 Jul 05 | 316 | Mars | R-130 | 145-192 | 0.94 | 2021 Apr 14 | 717 | Mars | R-130 | 120-172 | 0.94
2016 Jul 06 | 317 | Mars | B1-130 | 110-124 | 0.99 | 2021 Apr 20 | 720 | Mars | B1-130 | 65-126 | 1.00
2016 Jul 06 | 317 | Mars | B2-105 | 51-55 | 1.00 | 2021 Apr 20 | 720 | Mars | R-105 | 150-155 | 0.95
2016 Jul 06 | 317 | Mars | B2-130 | 56-71 | 1.00 | 2021 Apr 20 | 720 | Mars | R-130 | 145-205 | 0.94
2016 Jul 06 | 317 | Mars | R-105 | 118-130 | 1.13 | 2021 Apr 21 | 721 | Mars | B1-105 | 86-105 | 1.01
2016 Jul 06 | 317 | Mars | R-130 | 129-205 | 1.09 | 2021 Apr 21 | 721 | Mars | B2-105 | 59-72 | 1.02
2017 Mar 01 | 380 | Callisto | B1-105 | 71-94 | 1.01 | 2021 Apr 21 | 721 | Mars | R-105 | 145-205 | 0.93
2017 Mar 01 | 380 | Callisto | B1-130 | 71-105 | 1.02 | 2022 Mar 23 | 843 | Mars | B1-105 | 65-98 | 1.06
2017 Mar 03 | 382 | Callisto | B1-130 | 91-124 | 1.00 | 2022 Mar 23 | 843 | Mars | B2-130 | 50-70 | 1.12
2017 Jul 26 | 422 | Uranus | B1-105 | 69-72 | 1.03 | 2022 Mar 23 | 843 | Mars | R-105 | 142-188 | 1.15
2017 Jul 28 | 424 | Uranus | B1-105 | 70-108 | 1.01 | 2022 Mar 23 | 843 | Mars | R-130 | 125-178 | 1.16
2018 Nov 06 | 524 | Mars | B1-105 | 65-105 | 0.85 | 2022 Mar 28 | 846 | Mars | B1-130 | 84-90 | 1.21
2018 Nov 06 | 524 | Mars | B2-105 | 50-68 | 0.89 | 2022 Mar 28 | 846 | Mars | B2-105 | 51-72 | 1.11
2018 Nov 06 | 524 | Mars | R-105 | 115-205 | 0.87 | 2022 Mar 28 | 846 | Mars | R-105 | 118-185 | 1.12
2018 Nov 07 | 525 | Mars | B1-130 | 65-125 | 0.95 | 2022 Mar 28 | 846 | Mars | R-130 | 162-169 | 1.20
2018 Nov 07 | 525 | Mars | R-130 | 145-205 | 0.97 | 2022 Mar 29 | 847 | Mars | B1-130 | 85-130 | 1.16
2018 Nov 08 | 526 | Mars | B1-130 | 119-126 | 0.86 | 2022 Mar 29 | 847 | Mars | B2-105 | 49-53 | 1.18
2018 Nov 08 | 526 | Mars | B2-130 | 51-71 | 0.92 | 2022 Aug 25 | 847 | Mars | R-105 | 118-122/182-202 | 1.16
2018 Nov 08 | 526 | Mars | R-130 | 120-175/200-205 | 0.90 | 2022 Mar 29 | 847 | Mars | R-130 | 167-205 | 1.19
2018 Nov 09 | 527 | Mars | B1-105 | 68-74 | 0.92 | 2022 Aug 25 | 906 | Mars | B1-105 | 65-105 | 0.92
2018 Nov 09 | 527 | Mars | B2-105 | 50-74 | 0.95 | 2022 Aug 25 | 906 | Mars | B1-130 | 65-128 | 1.00
2018 Nov 09 | 527 | Mars | R-105 | 115-188 | 1.03 | 2022 Mar 29 | 906 | Mars | R-105 | 145-202 | 1.01
2019 Feb 27 | 548 | Mars | B1-130 | 65-110 | 0.98 | 2022 Aug 25 | 906 | Mars | R-130 | 143-205 | 1.09
2019 Feb 27 | 548 | Mars | B2-105 | 50-66 | 0.98 |  |  |  |  |  |

####  3.7.2 Atmospheric models

The correction for the atmospheric absorption and telluric lines is paramount
to obtain accurate response curves. If the telluric lines are not accurately
corrected they produce bumps in the response curve which can significantly
change the response along a large wavelength range. This was the case of the
response curves obtained in 2019 which did not benefit from the knowledge of
the amount of precipitable water vapor during the observations (see Section
3.6). In this work we make use of this information and we also use a model of
the atmosphere more recent than ATRAN, since we discovered that ATRAN contains
several lines which are not detected in our observations (see top panel of
Fig. 10). The ATRAN models distributed with the pipeline have been empirically
corrected by manually removing these extra-features. In the study of the
spectral scans, however, to be more accurate we computed a model for each
frame of the scan, with different values of altitude, telescope elevation, and
precipitable water vapor. We used the AM model (version 12.2)
555https://lweb.cfa.harvard.edu/~spaine/am which better reproduces the
atmospheric transmission with parameters close to the one used by ATRAN. We
used a 2 layer model assuming concentrations of 450, 0.28, 0.075, 1.895,
105$\cdot 10^{3}$ $\mu$mol/mol fraction in dry air for the CO2, N2O, CO, CH4,
and O2 (coupled and uncoupled) gases, respectively. The default value for O3
was assumed to be 320 DU (a Dobson unit is equivalent to 2.687$\cdot 10^{16}$
molecules/cm2). To compute the column density of the gases and water vapor in
the different layers, we used the profile of the mixing ratios of O3, H2O, and
gas mix used by the ATRAN models. We therefore generated atmospheric
transmission curves very similar to those computed with ATRAN, but without the
features which are not found in our data, as shown in the top panel of Fig.
10.

In the wavelength range 50-52$\mu$m, crucial to calibrate the response since
it contains the important [OIII]51.81$\mu$m line, the AM and ATRAN models do
not correctly reproduce the profile of two telluric lines. To obtain a better
match to the data we reduced the absorption to 60% of the value predicted by
the AM models. Finally, to obtain smoother responses, we did not consider data
for which the atmospheric transmission was lower than 50%. Such wavelength
intervals are left blank in the response figures (see, e.g., bottom panel of
Fig. 10).

Figure 10:  Top: Three examples of lines in the ATRAN model which are not seen
in the data and are not present in the AM models. The data have been
renormalized to the maximum of the transmission models. Bottom: Effects of
changing the O3 level in the atmospheric correction. The standard value of 320
DU overcorrects the ozone features in some of the observations. A lower O3
value dramatically reduces the noise in the data of this 2016 (flight 312)
observation of Mars. The curve with higher O3 correction has been shifted by
adding $0.5\cdot 10^{-11}$ ADU/Hz/Jy to better show the difference in the
correction.

Another advantage of using the AM code is the ability to vary the quantity of
ozone used to compute atmospheric models. In previous derivations, when ATRAN
was used to do the atmospheric corrections, the value assumed was the standard
320 DU. However, in different SOFIA observations the column of ozone can vary
since the flights covered different parts of the globe in different seasons.
When computing the response, we selected the values of ozone which better
corrected the response curves. As shown in the bottom panel of Fig. 10,
assuming a value of ozone too high can lead to a significant increase in the
noise of the response. In the case shown, a much better correction is obtained
by lowering the O3 column to 200 DU. Unfortunately, during the flights we did
not monitor the O3 column as we did with the water vapor. So, this correction
can be done only with spectral scans where the effect is easily quantifiable.
This is potentially a problem for [CII]158$\mu$m line observations since an
ozone feature very close to this wavelength can be overcorrected generating a
spurious emission line which, at certain redshifts, can be erroneously
interpreted as [CII] emission.

Figure 11:  Response curves for the observation of Mars in the red array
(dichroic 105$\mu$m) with the new filter window (years 2018-2022). The color
code refers to the flight number in the legend. The top panel shows the
response curves which are scaled to a common curve on the middle panel. Most
of the uncertainty in flux calibration comes from the flight-to-flight
multiplicative variation of the response. The bottom panel shows the residuals
of the fit with a Chebyshev polynomial (black line).The error in calibration
lowers from 12% to 6% after scaling the curves.

####  3.7.3 Response curves

Figure 12:  Response curves for all the arrays/orders/dichroics and periods
pre- and post- filter window change.

Two sets of response curves have been derived using the observations listed in
Table 2. In Fig. 11 we show the different response curves derived for the red
channel with data from 2018-2022, i.e. after the filter window change. Each
color corresponds to a response curve obtained in a different flight as
specified in the legend. The top panel shows the original response curves,
while the middle one shows the same curves after scaling them to a common
median curve. The response curves obtained in different flights are in fact
very similar and only differ by a multiplicative factor. The scaling factors
used to obtain the response curves in Fig. 12 are reported in the column of
Table 2 with title ’Scaling’. The fact that such curves obtained in different
flights coincide so well after scaling them to a median curve shows that the
limiting factor for the accuracy of the flux calibration is the scatter
between different flights. The error in calibration could be reduced by half
if we were able to obtain calibration curves for each flight (see example in
Fig. 11). Restrictions in the availability of calibrators and the urgency to
efficiently use the available science time limited the number of calibrators
observed. Moreover, the internal calibrator was usable only in laboratory
settings since it was never approved for flights. There was, therefore, no way
to calibrate in flux every night of observation. The accuracy in the flux
calibration of FIFI-LS is evaluated via the distribution of scaling factors
used to match each flight to a common behavior.

The response curves for all the array/orders/dichroics combinations in the two
epochs (before and after the change of the filter window) are shown in Figure
12. Dots with different colors correspond to data taken in different flights.
The response for the red, blue $1^{st}$ and $2^{nd}$ orders are shown in red,
blue, and purple, respectively. They are obtained by fitting Chebyshev
polynomials to the data. In the case of the 1st order in the blue, dichroic
130$\mu$m, the curves have been fitted with two polynomials to better match
the cuspid around 90$\mu$m which is due to a dip in the transmission of the
130$\mu$m dichroic. For the old filter window, the $1^{st}$ order has more
scatter since calibrators fainter than Mars are used to obtain the response
(Callisto and Uranus).

####  3.7.4 Differences with previous release

The response curves used before this paper were done in 2019 and have been
used to process data until 2022. Since many FIFI-LS papers used them in their
analyses, we discuss here the main variations between the previous and this
final release for the main lines observed in the blue and red arrays. We
remind that, since the instrumental fluxes are divided by the response to
calibrate the flux in physical units, a lower response will correspond to a
higher flux and vice versa.

Changes are negligible for observations in the red array done after the filter
window change (2018-2022, corresponding to Flight 524 and later). For the old
filter, the new response is approximately 9% lower than the previous one with
the 130$\mu$m dichroic and 6% lower with the 105$\mu$m dichroic.

For the blue array, there are differences even with the new filter window. For
the old filter window (data pre-2018), the 1st order in the blue is 10% and
12% lower than before with the 105 and 130$\mu$m dichroics, respectively. For
the 2nd order the difference is smaller since the new response is 5% lower in
the two dichroics. In the case of the new filter window (data between 2018 and
2022), the effect is similar. The new response is 12% lower than the previous
one for the 1st order for the two dichroics. For the 2nd order the difference
is smaller, the new response is 5% and 3% lower than the previous response
with the 130 and 105$\mu$m dichroics.

Figure 13: Cross-correlation of FIFI-LS and PACS fluxes in several apertures
of common targets showing the excellent agreement between the two instruments
in the red (top) and blue (bottom) arrays. The dashed blue horizontal line
corresponds to the median of the values. The data in this Figure are reported
in Table 4.

####  3.7.5 Flux cross-correlation with PACS/Herschel

A few cross-correlations of the [CII]158$\mu$m line fluxes measured with FIFI-
LS and PACS available in literature show a good agreement between the two
instruments (Reach et al., 2020; Sutter & Fadda, 2022a). In this section we
extend this comparison to several other objects observed with Herschel/PACS
and SOFIA/FIFI-LS. Most of the PACS observations considered were done with
unchopped spectroscopy since it was impossible to chop in extended emitting
regions with Herschel. When comparing these observations to FIFI-LS we took
care of reprocessing the PACS data using the transient correction pipeline
(Fadda et al., 2016) and its recent updates in Sutter & Fadda (2022b). As
already shown by Sutter & Fadda (2022a) in the case of NGC 7331, the PACS
archival data can be significantly off in flux calibration since they are
based on the internal calibrators rather than on the more stable telescope
background as is the case of normal chop-nod observations. Such calibrators
have a response which depends on memory effects of the detectors and can be
off by 20% to 90% in an unpredictable way. In one of the cases we examined
(NGC 2146), the nucleus of the galaxy was observed at 158$\mu$m with PACS in
the two modes : chop-nod and unchopped. A direct comparison of the flux from
the central part between the two observations shows that the unchopped flux is
80% higher than the chop-nod flux. The difference virtually disappears when
using the transient-correction pipeline. In this case, the measured flux
agrees very well with that measured by SOFIA/FIFI-LS as shown in Fig. 13. We
also noticed that the astrometry was incorrect by a few arcseconds in a few
PACS observations. Before measuring the flux, in the case of NGC 2146 and
M100, we corrected the astrometry by using the WISE channel 4 image to re-
center the central peak of the [CII] emission to the nucleus of the galaxies.
To obtain Fig. 13 we first degraded the PACS cube to the same spatial
resolution of the FIFI-LS cube. Then, we measured the flux in several
apertures fitting the lines with a pseudo-Voigt profile with the interactive
software sospex 666available at https://github.com/darioflute/sospex (Fadda &
Chambers, 2018). In the case of the FIFI-LS blue array, we used a Gaussian
which better approximates the line profile (see Section 3.4). The measurements
from the two instruments agree very well inside the errors, except for the
nucleus of M82 which has several FIFI-LS measurements with discordant fluxes,
probably taken in flights where the deviation from the median response was at
its highest values. The two PACS measurements, the first of them done during
the verification phase, are in very good agreement. However, the FIFI-LS flux
reported in Fig. 13 measured on the coaddition of the different flights does
not differ significantly from the one measured with PACS. The comparison
between PACS and FIFI-LS for the blue array is more difficult since the field-
of-view of FIFI-LS is much smaller and many parallel observations of [CII]
maps have a shallower and sometimes incomplete coverage. Of the two most
intense oxygen lines, we choose to focus on the [OIII] line at 88.3$\mu$m
since the [OI] line at 63.2$\mu$m is contaminated by a telluric line. Since
the quality of the FIFI-LS data is not optimal in the 1st order because of the
slightly skewed line profile, the scatter of these observations is larger than
that of the comparison of [CII] measurements in the red array. Moreover, there
are not many regions observed by both instruments with high signal-to-noise
ratio. In fact, although many of the extended galaxies observed with PACS in
[CII] have parallel data in [OIII], the parallel data are shallower (due to
the different field of view) and usually only the nucleus is detected. Only in
the case of NGC 6946 a few deep observations of starforming regions have been
obtained. Generally, the measurements of PACS and FIFI-LS agree well with one
exception: NGC 253. The observation of NGC 253 has been repeated twice with
FIFI-LS with similar results, while the Herschel/PACS observation was done in
chopping mode. We suspect that the discrepancy in flux with the FIFI-LS
measurement is due to contamination in the sky position of the PACS
observation.

The set of data considered in the comparison, as well as the apertures and the
flux measurements are reported in Table 4 in Appendix C. The errors reported
in Table 4 are computed by fitting the spectra and their errors with the line
profiles. Since the dispersion of the ratios is less than 10% and considering
the spread in response found studying the response curves (see Sec. 3.7.3), it
is reasonable to assume that the calibration is accurate at 15% or better
across the entire wavelength range of the instrument.

###  3.8 Sensitivity

Figure 14: Effect of the subtraction of the open pixel on two consecutive
ramps in the blue channel. The ramps of the 16 pixels in the central spaxel of
a flat observation in the blue channel show some correlated noise (top panel).
After subtracting the signal from the open pixel, plotted in black, most of
the correlated noise disappears (see bottom panel).

####  3.8.1 Bias subtraction

The estimates of the sensitivity are based on the noise of the integration
ramps. When studying the noise in the ramps we noticed that there was some
level of correlation between the noise of different pixels in the same spatial
module. The cause of this noise is unknown but the analysis can be
dramatically improved by subtracting the signal of the open pixel which does
not see the sky. This procedure is similar to the bias subtraction done with
optical CCDs by using a lateral band of the CCD which is not exposed to the
sky. By subtracting the open pixels, the noise in the ramps is drastically
reduced. Figure 14 shows the effect of the subtraction in the ramps for the
different pixels of the central spaxel (number 12). By analyzing the reduction
of the noise in the final spectra, we found out that the bias subtraction
reduced the noise by at least 10%. For this reason, the option of bias
subtraction has been added to the FIFI-LS pipeline in 2020 and it is now used
by default.

Figure 15: Continuum and line sensitivities for the FIFI-LS instrument in the
three different bands and two dichroics with the latest filter window at
4$\sigma$ with an exposure time of 900 s. The sensitivity of PACS on Herschel
is shown for comparison as a grey line. The green bands mark the wavelength
ranges which were not observable with PACS on Herschel.

####  3.8.2 Continuum and line sensitivities

The sensitivity of FIFI-LS in the different arrays/orders have been computed
by estimating the errors in the ramp fitting with observations of the internal
calibrator and applying the response curves to these limiting fluxes. The
mathematical details of the computations used to obtain these curves are
presented in the Appendix A. Figure 15 shows the curves for the three
different bands covered by FIFI-LS (red, blue in 1st and 2nd order) and the
two possible dichroics. The solid curves correspond to the 105$\mu$m dichroic,
while the dashed ones correspond to the 130$\mu$m dichroic. The shaded bands
are the uncertainties for the estimated curves.

In the figure, the green bands mark the regions of the spectrum which were not
observable with PACS on Herschel. In particular, the observation of the
important line of [OIII] at 51.81$\mu$m was made possible by the upgrade of
the filter window in 2018. Depending on the redshift of the object, this line
was observed with the dichroic which had the best sensitivity (130 at low
redshift, 105 for targets with $cz>4500$ km/s).

For comparison, we plotted with grey lines the sensitivity of the PACS
instrument on Herschel, which was very similar to FIFI-LS, but was operating
from space with a slightly bigger telescope. The main difference between the
two instruments is in the blue array, since PACS was using the 2nd order of
the grating while FIFI-LS used the 1st order of a grating optimized for its
wavelength range. Moreover, PACS had the same pixel size for the two arrays,
while FIFI-LS had pixels of 6” and 12” size for the blue and red array,
respectively. Because of these reasons, the line sensitivity in the blue is
only slightly worse for FIFI-LS , while PACS is more sensitive in the red. We
stress here that, although the sensitivity is similar, the observations with
FIFI-LS are affected by the atmospheric transmission and telluric features
which sometimes make the observations rather challenging and the real
sensitivity worse than what is shown in Figure 15.

##  4 Summary

We presented the characterization and absolute flux calibration of FIFI-LS
using measurements made in the laboratory and in flight. We analyzed the non-
linearity of the detectors concluding that the effect is minimal. Most of the
systematic variations are, in fact, absorbed by the absolute flux calibration
while the residual noise is around 1%, a value much lower than the error in
flux calibration. We presented the procedure used to estimate the spatial and
spectral flats of the detectors. We analyzed laboratory data to study the
profile of unresolved lines for the two arrays and two orders in the blue.
Lines are slightly asymmetric in the blue. In particular, the blue 1st order
has a bump on the long wavelength side and it is best fitted with skewed
Gaussian. Pseudo-Voigt profiles are a good approximation for the red channel
and the blue 2nd order. Formulae to compute the spectral and spatial
resolution of FIFI-LS are derived. In particular, the spatial resolution has
been studied by observing bright point-sources. The technique used to estimate
the precipitable water vapor in flight is discussed and the results of the
measurements are shown as a function of altitude and season. They clearly show
a seasonal effect on the precipitable water vapor. We presented the study of
the response of the instrument done by using sky calibrators. New response
curves are derived with a much improved correction of telluric lines which
makes use of the knowledge of precipitable water vapor and a variable ozone
column. The response is shown to be varying by a multiplicative factor between
different flights, a fact that contributes to the uncertainty in the flux
calibration. Because of this, the uncertainty on calibration is around 15%.
The availability of calibrators on each flight would have reduced the
uncertainty by a factor two. A cross-correlation between fluxes estimated from
PACS and FIFI-LS observations of the same sky regions show a very good
agreement between the flux calibration of the two instruments, provided that
the transient-correction pipeline is used to reprocess PACS unchopped data
rather than using the archival products. We show, in fact, that the flux of
the archival products of PACS unchopped observations can be off up to a factor
two and that the difference with the FIFI-LS fluxes disappears when the flux
is calibrated using the telescope background as reference.

Finally, we presented updated sensitivity curves for FIFI-LS based on the
noise on the ramps after subtracting the signal from the bias pixel.

We thank the anonymous referee for many useful comments and suggestions. This
paper was based on observations made with the NASA/DLR Stratospheric
Observatory for Infrared Astronomy (SOFIA) and with Herschel. SOFIA was
jointly operated by the Universities Space Research Association, Inc. (USRA),
under NASA contract NNA17BF53C, and the Deutsches SOFIA Institut (DSI) under
DLR contract 50 OK 0901 to the University of Stuttgart. Herschel was an ESA
space observatory with instruments provided by European-led P.I. consortia and
important NASA participation.

##  Appendix A Mininum detectable continuum and line fluxes

In this section we derive the formulae used to estimate the sensitivity of
FIFI-LS in the different filter/order combinations. In the case of the minimum
detectable continuum flux, we consider the flux which is observed after
coadding the 16 pixels corresponding to each spaxel, or spatial module. The
limiting factor for detection is the dispersion of the ramp fits
($\sigma_{r}$). Since each series of ramps has an exposure time $t_{exp}$,
considering a total integration time of 900 s and a 4$\sigma$ detection, the
minimum continuum flux detected is:

$MDCF(\lambda)[Jy]=\frac{4\sigma_{r}(\lambda)}{\sqrt{16}}\frac{\sqrt{\frac{t_{exp}[s]}{900s}}}{\rho(\lambda)}=\sqrt{\frac{t_{exp}[s]}{900s}}\frac{\sigma_{r}(\lambda)[ADU/Hz]}{\rho(\lambda)[ADU/Hz/Jy]},$
(A1)

where $\rho(\lambda)$ is the response of the instrument at the wavelength
$\lambda$.

To compute the minimum detectable line flux, in the case of an unresolved
line, we have to take into account the number of pixels involved in the
detection of the flux. In practice, we have to consider the optimal interval
which allows one to have the highest signal-to-noise ratio to detect the line.
If we consider a line with a Gaussian profile, which is a good approximation
in the case of FIFI-LS:
$F(\lambda)=\frac{F_{0}}{\sqrt{2\pi}\sigma}e^{-\frac{(\lambda-\lambda_{0})^{2}}{2\sigma^{2}}}$,
by integrating the line inside the wavelength interval of size $2L$, we obtain
a signal-to-noise ratio of:

$S/N=\frac{\frac{1}{\sqrt{2\pi}\sigma}\int_{\lambda_{0}-L}^{\lambda_{0}+L}F_{0}e^{-({\lambda-\lambda_{0}})^{2}/(2\sigma^{2})}d\lambda}{\sqrt{\frac{2L}{\delta_{pix}}}\sigma_{pix}(\lambda)\delta_{pix}}=\frac{\frac{1}{\sqrt{2\pi}\sigma}2\int_{0}^{L}F_{0}e^{-\lambda^{2}/(2\sigma^{2})}d\lambda}{\sqrt{\frac{2L}{\delta_{pix}}}\sigma_{pix}(\lambda)\delta_{pix}}=\frac{F_{0}}{\sqrt{\frac{2\sqrt{2}\sigma}{\delta_{pix}}}\sigma_{pix}(\lambda)\delta_{pix}}\frac{erf(\frac{L}{\sigma\sqrt{2}})}{\sqrt{\frac{L}{\sigma\sqrt{2}}}}$
(A2)

where $erf(z)=\frac{2}{\sqrt{\pi}}\int_{0}^{z}e^{-t^{2}}dt$. In the
denominator we have the number of pixels in the interval $2L/\delta_{pix}$,
with $\delta_{pix}$ the size of the pixel in wavelength and $\sigma_{pix}$ the
noise in the single spectral pixel measured on ramps. The noise is multiplied
by the width of the pixel to get the integrated flux in the pixel. The
function $erf(x)/\sqrt{(}x)$ has a maximum at
$x=\frac{L}{\sigma\sqrt{2}}\approx 1$, which means that the optimal S/N is
reached by integrating along an interval of $2\sqrt{2}\sigma$.

Inside this interval, 84% of the total flux is detected. The S/N in the
optimal aperture is therefore:

$S/N=\frac{F_{ap}}{\sqrt{\frac{2\sqrt{2}\sigma}{\delta_{pix}}}\sigma_{pix}(\lambda)\delta_{pix}}$
(A3)

Now, since the spectral resolution is defined as: $R=\frac{\lambda}{FWHM}$,
assuming a Gaussian line of dispersion $\sigma$, since $FWHM=2\sqrt{2\ln
2}\sigma$, this means: $\sigma=\frac{\lambda}{2\sqrt{2\ln 2}R}$. Therefore,
the optimal interval to measure the flux of the line is:
$\Delta\lambda=2\sqrt{2}\sigma=\frac{\lambda}{\sqrt{\ln 2}R}$. So, the number
of pixels in the optimal interval is: $N_{pix}=\frac{\lambda}{\sqrt{\ln
2}R\delta_{pix}}$, where $\delta_{pix}$ is the spectral width of a pixel.

Figure 16: Left: Optimal width in pixels for detecting an unresolved line.
Right: Total flux fraction of a point source centered on the array detected by
the central spaxel. The fraction for PACS/Herschel is shown for comparison.
The FIFI-LS fraction is smaller than PACS in the blue array since its smaller
spaxel size is tailored to the PSF size.

The left panel in Fig. 16 shows that the number of pixels corresponding to the
interval for optimal detection is between 3 and 4. At this point, we can
compute the flux measured at a certain S/N by inverting the previous equation:
$F_{ap}=S/N\sqrt{\frac{2\sqrt{2}\sigma}{\delta_{pix}}}\sigma_{pix}(\lambda)\delta_{pix}$
By substituting $\sigma$ with $\frac{\lambda}{2\sqrt{2\ln 2}R}$ and
$\sigma_{pix}(\lambda)$ with $\sigma_{pix}(\nu)\frac{c}{\lambda^{2}}$ and
using $S/N=4$, we obtain:

$MDLF[10^{-17}W/m^{2}]=4\sqrt{\frac{\delta_{pix}[\mu m]}{R\sqrt{\ln
2}}}\frac{\sigma_{pix}(\nu)[Jy]\cdot c[km/s]}{\lambda^{3/2}[\mu m]}$ (A4)

##  Appendix B Flux fraction in a spaxel

When comparing the two similar instruments FIFI-LS and PACS on Herschel, it is
important to remember that they had different spatial resolutions and sky
pixel sizes. The spaxel size of FIFI-LS has been set to capture most of the
flux of a point source, since they are comparable to the FWHM of the point
spread function. It is nevertheless important to realize that a spaxel will
not capture all the flux of a point source, but it will lose some fraction of
it depending on the wavelength where it is detected. The right panel of Fig.
16 shows how the fraction of flux in the central pixels varies in the two
detectors (red and blue) at different wavelengths, assuming that the source is
centered on the spaxel. The curves for PACS on Herschel are shown for
comparison. While for the red array they are almost equivalent since the
better spatial resolution of PACS compensates for its smaller pixel, in the
case of the blue array FIFI-LS intercepts less flux since it uses a much
smaller spaxel better adjusted to the PSF in the blue, while PACS used the
same spaxel size for the two arrays, therefore intercepting almost all of the
flux in the blue. We also remind that most of the PACS observations were done
without or with very limited dithering, while all the FIFI-LS observations
included abundant spatial dithering. This means that, although the point
spread function of PACS is theoretically better, it is sometimes impossible to
recover its shape with limited or no spatial dithering because the size of the
pixel is not small enough to satisfy the Nyquist-Shannon sampling theorem.
Therefore, the FIFI-LS images can appear more defined than those taken with
PACS.

##  Appendix C Additional tables

Table 3 reports the values of spatial and spectral resolution for the most
important lines observed with FIFI-LS at reference wavelength, as well as the
instantaneous coverage of the 16 spectral pixels.

Table 3: Spatial and spectral resolution for the most important lines observable with FIFI-LS. Line | Rest wav | Array | Spatial FWHM | Central pixel | R | Spectral FWHM | Instant. coverage
---|---|---|---|---|---|---|---
Name | [$\mu$m] | Order | [arcsec] | flux fraction |  | [km/s] | [km/s] | [$\mu$m]
[OIII] | 51.8145 | B2 | 6.6 | 51% | 792 | 378 | 1838 | 0.32
[NIII] | 57.3170 | B2 | 6.7 | 47% | 1004 | 299 | 1526 | 0.29
[OI] | 63.1837 | B2 | 7.4 | 43% | 1326 | 226 | 1242 | 0.26
[OIII] | 88.3560 | B1 | 8.6 | 35% | 621 | 482 | 2341 | 0.69
[NII] | 121.8976 | B1 | 11.8 | 20% | 1016 | 295 | 1351 | 0.55
[NII] | 121.8976 | R | 11.8 | 59% | 808 | 371 | 2343 | 0.95
[OI] | 145.5254 | R | 14.1 | 47% | 1071 | 280 | 1797 | 0.87
[CII] | 157.7409 | R | 15.3 | 42% | 1207 | 248 | 1561 | 0.82

Table 4 contains the line fluxes measured inside circular apertures from
sources observed both by PACS and FIFI-LS.

Table 4: PACS and FIFI-LS flux cross-correlation. Object | Line | SOFIA | PACS AOR | Apertures
---|---|---|---|---
Name |  | flights | IDs | # | Center [J2000] | r | FIFI-LS | PACS
|  |  | 1342000000+ |  | [J2000] | [as] | [1015 W/m2] | [1015 W/m2]
M51 | [CII] | 281,282,283, | 211188 | 1 | 13:29:50.52 +47:11:35.00 | 10 | 1.14 $\pm$0.05 | 1.16$\pm$0.01
|  | 284,285,287, |  | 2 | 13:29:52.33 +47:11:23.24 | 10 | 0.85 $\pm$0.07 | 0.85$\pm$0.01
|  | 380,381,382, |  | 3 | 13:29:55.40 +47:11:45.76 | 10 | 1.07 $\pm$0.03 | 1.09$\pm$0.01
|  | 383,384 |  | 4 | 13:29:51.82 +47:11:56.66 | 10 | 1.37 $\pm$0.03 | 1.37$\pm$0.02
|  |  |  | 5 | 13:29:52.68 +47:10:46.90 | 10 | 0.43 $\pm$0.05 | 0.43$\pm$0.01
|  |  |  | 6 | 13:29:52.10 +47:12:42.63 | 10 | 0.72 $\pm$0.01 | 0.71$\pm$0.01
M82 | [CII] | 202,280,283, | 187205 | 1 | 09:55:51.49 +69:40:45.23 | 20 | 106$\pm$1 | 109$\pm$ 1
|  | 287,565,566 |  |  |  |  |  |
M100 | [CII] | 572,573, | 223733 | 1 | 12:22:54.88 +15:49:20.40 | 11 | 1.50$\pm$0.06 | 1.52$\pm$0.01
|  | 638,640,663 |  | 2 | 12:22:51.60 +15:49:38.42 | 11 | 0.50$\pm$0.04 | 0.48$\pm$0.01
|  |  |  | 3 | 12:22:48.72 +15:50:04.43 | 11 | 0.21$\pm$0.02 | 0.20$\pm$0.01
NGC891 | [CII] | 549,635, | 214874, 214879 | 1 | 02:22:36.04 +42:22:10.04 | 8 | 1.39$\pm$0.02 | 1.38$\pm$0.01
|  | 648,639 |  | 2 | 02:22:37.47 +42:22:49.94 | 8 | 1.14$\pm$0.02 | 1.15$\pm$0.01
NGC2146 | [CII] | 199,567,568, | 220742 | 1 | 06:18:38.33 +78:21:22.21 | 10 | 11.2$\pm$0.1 | 11.3$\pm$0.1
|  | 571,638 |  |  |  |  |  |
NGC6946 | [CII] | 202,203,247, | 223388 | 1 | 20:34:58.15 +60:10:19.21 | 10 | 0.28$\pm$ 0.01 | 0.29$\pm$ 0.01
|  | 253,281,284, |  | 2 | 20:34:52.51 +60:09:14.50 | 10 | 2.82$\pm$ 0.04 | 2.83$\pm$ 0.08
|  | 285,286 |  | 3 | 20:34:48.34 +60:08:24.24 | 10 | 0.39$\pm$ 0.02 | 0.39$\pm$ 0.01
|  |  |  | 4 | 20:34:43.97 +60:07:24.79 | 10 | 0.39$\pm$ 0.02 | 0.40$\pm$ 0.01
NGC7331 | [CII] | 632,634, | 222579 | 1 | 22:37:03.60 +34:24:29.94 | 7.8 | 0.57$\pm$ 0.02 | 0.57$\pm$ 0.01
|  | 640,681 |  | 2 | 22:37:04.29 +34:24:42.51 | 7.8 | 0.43$\pm$ 0.02 | 0.42$\pm$ 0.01
|  |  |  | 3 | 22:37:05.55 +34:24:41.27 | 7.8 | 0.52$\pm$ 0.02 | 0.53$\pm$ 0.01
|  |  |  | 4 | 22:37:03.94 +34:24:57.45 | 7.8 | 0.36$\pm$ 0.01 | 0.36$\pm$ 0.01
|  |  |  | 5 | 22:37:02.97 +34:24:45.19 | 7.8 | 0.51$\pm$ 0.02 | 0.50$\pm$ 0.01
|  |  |  | 6 | 22:37:04.50 +34:25:11.97 | 7.8 | 0.47$\pm$ 0.03 | 0.47$\pm$ 0.01
|  |  |  | 7 | 22:37:02.68 +34:25:01.07 | 7.8 | 0.49$\pm$ 0.02 | 0.49$\pm$ 0.01
|  |  |  | 8 | 22:37:05.22 +34:24:56.44 | 7.8 | 0.59$\pm$ 0.02 | 0.59$\pm$ 0.00
30DOR | [CII] | 310 | 270358,231283,231282, | 1 | 05:38:49.27 -69:04:43.14 | 24 | 60.8$\pm$ 0.4 | 61$\pm$ 2
|  |  | 222085,222088,222089 | 2 | 05:38:33.06 -69:06:25.19 | 24 | 33.5$\pm$ 0.8 | 33.5$\pm$ 0.5
|  |  | 222094,231279,231281 | 3 | 05:38:59.18 -69:04:06.08 | 24 | 38.3$\pm$ 0.9 | 37.7$\pm$ 0.9
N81 | [OIII] | 842 | 253769 | 1 | 01:09:12.76 -73:11:39.07 | 13 | 7.55$\pm$0.15 | 7.15$\pm$0.02
M51 | [OIII] | 384 | 211191 | 1 | 13:29:50.81 +47:11:56.88 | 10 | 0.14$\pm$0.05 | 0.13$\pm$ 0.01
IC10 | [OIII] | 382 | 214367 | 1 | 00:20:27.84 +59:17:38.30 | 15 | 6.9 $\pm$ 0.2 | 6.42 $\pm$ 0.02
NGC6946 | [OIII] | 719 | 223762 | 1 | 20:34:52.40 +60:09:12.89 | 10 | 0.52$\pm$0.03 | 0.52 $\pm$ 0.01
| [OIII] | 721 | 222248 | 2 | 20:35:25.40 +60:09:57.96 | 12 | 1.15$\pm$0.01 | 1.17$\pm$0.01
| [OIII] | 737,803 | 223377 | 3 | 20:35:16.89 +60:10:58.49 | 5 | 0.17$\pm$0.02 | 0.16$\pm$0.01
NGC891 | [OIII] | 635,638,639 | 223762 | 1 | 02:22:37.15 +42:22:42.81 | 20 | 0.92$\pm$0.09 | 0.92$\pm$0.02
NGC253 | [OIII] | 250,525 | 199415 | 1 | 00:47:32.99 -25:17:17.43 | 10 | 7.5$\pm$0.1 | 5.7$\pm$0.05
M83 | [OIII] | 312,741 | 223811 | 1 | 13:36:53.84 -29:53:06.93 | 15 | 0.54$\pm$0.03 | 0.55$\pm$0.01

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