# 8.1   Specifications

## 8.1.1   Instrument Overview

The High-resolution Airborne Wideband Camera (HAWC+) is a multi-wavelength far-infrared imager and polarimeter with continuum bandpasses from 40 um to 300 um. HAWC+ Total Intensity Imaging uses a filter wheel and a polarizing grid to split incoming light into two orthogonal components of lineal polarization, the reflected (R) and transmitted (T) rays. For Polarimetry Imaging, a rotating half-wave plate (HWP) is introduced before the filter wheels. The current state of the instrument includes a 64x40 array measuring the R polarization state and a 32x40 array for the T polarization state. HAWC+ observations are diffraction-limited with a spatial resolution of 5 to 20 arcsec and a field of view (FOV) of 2 to 8 arcmin. HAWC+ is currently not offering observations at 63 um (Band B).

### 8.1.1.1   Design

A schematic of the HAWC+ optical design is shown in Figure 8-1. Prior to entering the HAWC+ cryostat, light from the SOFIA telescope enters the set of warm fore-optics mounted outside the cryostat. The light is reflected from a folding mirror to a field mirror, capable of imaging the SOFIA pupil at the cold pupil inside the HAWC+ cryostat. After the fore-optics, light enters the cryostat through a 7.6 cm diameter high-density polyethylene (HDPE) window, then passing through a cold pupil on a rotatable carousel, a near-infrared blocking filters to define each bandpass and lenses designed to optimize the plate scale. The pupil carousel and the filter wheel are at a temperature of ~10 K. The carousel contains eight aperture positions, four of which contain half wave plates (HWPs) for HAWC+ bands, an open aperture whose diameter is matched to the SOFIA pupil, and three aperture options meant only for instrument alignment tests.

After the pupil carousel, the light passes through a wire grid that reflects one component of linear polarization and transmits the orthogonal component to the detector arrays (R and T arrays, respectively—see Figure 8-2). The polarizing grid is heat-sunk to the HAWC+ 1 Kelvin stage.

To perform polarimetry observations, a HWP matched to the band-pass is rotated (usually through four discrete angles) to modulate the incident light and allow computation of the Stokes parameters. The total intensity can be measured simply by removing the HWPs from the optical path and using the open pupil position, then summing the signal from the R & T arrays.

The 64x40 HAWC+ detector array is composed of two co-mounted 32x40 subarrays from NASA/GSFC and NIST. The detectors are superconducting transition-edge sensor (TES) thermometers on membranes with a wide-band absorber coating. The detector array is indium bump bonded to a matched array of superconducting quantum interference device (SQUID) amplifiers, all cooled to an operating temperature of ~0.2 K in flight.

Figure 8-1.

Figure 8-1. Schematic of the HAWC+ optics. Light from the SOFIA telescope is incident from the right. The field and folding mirrors are mounted on the HAWC+ cryostat but extend into the SOFIA Nasmyth tube. At the polarizing grid the light is split into two orthogonal components of linear polarization and detected at the two separate arrays.

Figure 8-2.

Figure 8-2. HAWC+ utilizes two coaligned arrays of TES detectors, each array receiving polarized light from the source either by reflection (the R array) or transmission (the T array). The R array is populated with two 32x40 subarrays separated by 2.0 pixels, referred to as R0 (top left) and R1 (top right). The arrays are coaligned such that R0 and T0 (bottom left) observe the same patch of sky. Polarization observations are only supported using the R0 and T0 subarrays, and therefore observations are limited to the left half of the nominal field of view, or 32x40 pixels. Total intensity observations are supported using the combined R0 and R1 field of view, or 64x40 pixels with a 2.0 pixel gap between them.

## 8.1.2   Performance

The absorbing coatings on the HAWC+ detector arrays were optimized to produce about 50% efficiency across the wide (40–300 μm) range of bandpasses. The TESs were designed to optimize the sensor time constants and background power at which they saturate, with the goal being operation at both laboratory and stratospheric background levels. The final design includes a superconducting transition temperature of ~0.3 K and a detector yield of > 50%. Measurements of detector noise show that their contribution to total measurement uncertainties is negligible such that noise levels are dominated by background photons from the atmosphere.

Measurements of the HAWC+ optical system in the laboratory are consistent with optical models, and flight data have confirmed that the observations are diffraction limited at all wavelengths.

Table 8-1 shows the Full Width Half Maxiumum (FWHM) of each bandpass as measured using Gaussian profiles, the finite size of the HAWC+ detectors, and a convolution across the measured filter bandpasses. The Instrumental Polarization (IP) of HAWC+ at each band is shown in terms of the normalized Stokes parameters, q and u, which were estimated using the observations of planets during several observing runs on November 2016 and May 2017. The IP is mainly derived from the tertiary mirror of SOFIA with the position angle of polarization perpendicular to the tertiary mirror direction. The filter transmission curves (text tables) are available as a zip file or individually from Table 8-1.

For polarimetry observations, the current configuration of HAWC+ lacks a second T polarization state array; as such, the field of view is reduced to approximately half in the largest side of the array, providing a 32x40 pixel size rather than 64x40 pixels (the first element of the Field of View in Table 8-1).  Total intensity observations are unaffected and can use the whole field of view via the R polarization state.

Table 8-1: Instrument Characteristics
Important: Sensitivity values were updated on June 15, 2018 to reflect final commissioning analysis based on Cycle 5 & Cycle 6 observations.
Instrument Characteristics
Parameter Units Band A Band C Band D Band E
Mean Wavelength (λ0) μm 53 89 154 214
Bandwidth (Δλ) - 9.01 16.91 33.88 42.8
Beam Size (FWHM) arcsec 4.85 7.8 13.6 18.2
Pixel Sizea arcsec 2.55 4.02 6.90 9.37
Total Intensity FOV arcmin 2.8x1.7 4.2x2.7 7.4x4.6 10.0x6.3
Polarimetry FOV arcmin 1.4x1.7 2.1x2.7 3.7x4.6 5.0x6.3
NESBb (photo) MJy sr-1 h1/2 18.8 6.3 1.6 0.8
MDCFc mJy 250 300 154 214
Mapping Speedd See footnote d 0.0027 0.029 1.1 7
MDCPFe % Jy 40 20 21 24
IPf q -0.0154 -0.0151 0.0028 -0.0129
u -0.0030 0.0090 0.0191 0.0111
MIfPg MJy sr-1 h1/2 28,000 6,000 2,000 1,300
Response Curve

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a The center-to-center spacing of the pixels; pixel sizes (the space taken up by the photon sensitive area) are smaller by 0.21 arcsec at 53 μm and 0.75 arcsec at 215 μm.
b Noise Equivalent Surface Brightness for S/N = 1 into a single HAWC+ beam (FWHM given here).
c Minimum Detectable Continuum Flux for a point source with S/N = 4 in a 900 second integration.
d Real scan rate required to achieve a given an NESB. Units: arcmin2 h-1 (MJy sr-1)-2
e Minimum Detectable Continuum Polarized Flux for a point source with a S/N = 4 in a 900 second integration.
fInstrumental Polarization estimated using the observations of planets during several observing runs. The uncertainty of the instrumental polarization is smaller than 0.003 in both Stokes q and u.
gMinimum total Intensity required to measure Polarization (MIfP) to an uncertainty level σp ≤ 0:3%. All chop/nod and polarization overhead values have been applied to this value.

HAWC+ point source sensitivities were updated on June 2, 2017 and the values given here are based on the in-flight performance of the instrument. Note that values used in previous SOFIA observing cycles (Cycles 4 & 5) were estimates that contained an error (approximately a factor of two) in the expected point source sensitivity, so proposals should be updated accordingly for Cycle 6 before submission.

All photometric sensitivity estimates assume 100% observing efficiency without chopping and nodding. These values are pre-flight estimates and subject to change after the HAWC+ instrument has been commissioned. The USPOT time calculator will estimate the correct overhead values for NMC.

Additionally, analysis of data obtained on flights suggest the sensitivity may be lower than expected. The MDCF values will be correspondingly higher than the predicted pre-flight ones shown in Table 8-1 and used in Figure 8-4. The SOFIA webpages should be checked for the most current information.

Entries in blue represent predicted values; Band B is currently unavailable due to saturation in the band but may be offered as shared risk in future cycles.

### 8.1.2.1   Filters

HAWC+ can produce images using continuum bandpasses in either Total Intensity Imaging or Polarimetry Imaging configurations. In Polarimetry Imaging, the dual-beam nature of HAWC+ allows for the simultaneous measurement of both orthogonal lineal polarization components and obtain the Stokes parameters I, Q, and U. In Total Intensity Imaging, the sum of the R and T arrays provides the total intensity, Stokes I. As the HWP are used in Polarimetry Imaging, there is a slight loss of sensitivity as the HWP transmission is < 100% and additional overhead is required to account for rotating the HWP.

Both observing modes can utilize any one of five filters (however, to reiterate, Band B is not currently available). Figure 8-3 shows transmission profiles including all filters for all bandpasses. The effective wavelengths and bandwidths averaged over the total filter transmission are given in Table 8-1.

Figure 8-3.

Figure 8-3.

### 8.1.2.2   Total Intensity Imaging Sensitivities

Observations with HAWC+ for measurements of Total Intensity can be performed using either on-the-fly scanning (OTFMAP, where the telescope moves continuously at rates of ~10–200 arcsec/second without chopping of the secondary mirror) or using rapid modulation (chopping ~ 5–10 Hz) of the secondary accompanied by slow nodding of the telescope. The chopping option consists of a two-position chop, parallel to the nod direction where the chop amplitude matches the nod amplitude (NMC).

Figure 8-4 and Table 8-1 present HAWC+ imaging sensitivities for point sources, surface brightness, and mapping speed through each bandpass. Surface brightness is measured in units of MJy/sr and is the intensity required for a S/N = 1 observation in a one-hour integration time averaged over a single HAWC+ beam. The Minimum Detectable Continuum Flux into a HAWC+ beam is that needed to obtain a S/N = 4 in 900 seconds of on-source integration time. Figure 8-4 plots the MDCF for both observing modes OTFMAP and NMC where the latter follows from the former based on overheads related to chopping and nodding the telescope. NMC and OTFMAP are covered extensively in Section 8.2.

Figure 8-4.

Figure 8-4. HAWC+ Sensitivity estimates in units of the Minimum Detectable Continuum Flux (MDCF) into a single HAWC+ beam. (Recall that the beam area changes with bandpass). Values plotted here take into account all expected overheads. For example, Table 8-1 gives an MDCF of 57 mJy at 53 μm in OTFMAP, but is plotted here as 66 mJy to account for a 75% array detector yield. For Polarimetry, the plotted data show the polarized intensity p x I, where p is the fractional polarization (not percent). Note: analysis of data obtained on flights suggest the sensitivity may be lower than expected. The MDCF values will be correspondingly higher than the predicted pre-flight ones shown in Table 8-1 and used in Figure 8-3.

HAWC+ time estimates should be made using the on-line exposure time calculator, SITE. Note that integration times scale as shown in Equation 8-1 and Equation 8-2 from the values in Table 8-1:

(Eq. 8-1) $t=(NESBσ)2$

(Eq. 8-2) $t=(900 s)(NESBσ)2$

where t is the integration time and σ is the desired sensitivity for S/N = 1, each in the appropriate units. For OTFMAP, a useful sensitivity value is the mapping speed given in Equation 8-3:

(Eq. 8-3) $M=dΩdt=γΩarrays2$

where γ is related to the filling factor, Ωarray is the solid angle of the HAWC+ detector array, and s is some measure of the instrument sensitivity (e.g., MDCF or NESB). The values in Table 8-1 are given for S/N = 1 in a one-hour integration time assuming γ = 1, while SITE and Figure 8-3 use a more realistic value γ = 0.75. The time to map an area Ω (≥ Ωarray) to a sensitivity level σ is given by Equation 8-4:

(Eq. 8-4)

Note that this scaling only applies to map areas larger than the array field of view.

Atmospheric transmission will affect sensitivity, depending on water vapor overburden as will telescope zenith angle and telescope emissivity. For the estimates in Table 8-1 and Figure 8-3 we use a precipitable water vapor of 7.3 μm, a 50° zenith angle, and a telescope emissivity of 15%.

### 8.1.2.3   Polarimetry Imaging Sensitivities

HAWC+ contains four monochromatic HWPs. For Bands C, D, and E, the HWP thicknesses are matched to the bandpass filters. The thickness of the Band A HWP is matched to a wavelength between those of Bands A (53 μm) and B (63 μm), approximately 58 μm. However, this slight mismatch should not introduce significant systematics into the system. For the pre-flight HAWC+ sensitivity estimate here, the total system polarization efficiency (HWP + polarizing grid + all other optics) is assumed to be 90% for all five passbands.

The polarization sensitivity σp follows from the imaging sensitivity σI so that Equation 8-5 is true:

(Eq. 8-5) $σP=σI2ηpI$

where I is the source intensity, ηp is the system polarization efficiency, and σp is measured in units of percent (%). The Minimum Detectable Continuum Polarized Flux (MDCPF) reported in Table 8-1 is the value σp x I above, and follows from the total intensity MDCF. USPOT will add overhead values appropriate to NMC mode for polarimetry.

For Polarimetry Imaging, another useful quantity is the Minimum total Intensity required in order to measure polarization (MIfP) to a given depth in a given time interval. Choosing σp = 0.3% allows a polarization S/N = 3 for a source polarization of 1%, a value not atypical of bright Galactic clouds and a likely lower limit for HAWC+ systematic uncertainties. Table 8-1 lists these values for a one-hour integration time in units of surface brightness for an extended source where, unlike other values in Table 8-1, all appropriate overhead values have been added.

HAWC+ time estimates should be made using the on-line exposure time calculator, SITE. Note that integration times scale as shown in Equation 8-6 and Equation 8-7 from the values in Table 8-1:

(Eq. 8-6) $t=(1 h)(MIfPI)2(0.3%σp)2$

(Eq. 8-7) $t=(900 s)(MDCPF4σpI)2$

where t is the integration time and σp is the desired sensitivity for S/N = 1, each in the appropriate units.

A simple estimate for the polarization angle uncertainty is given by Equation 8-8:

(Eq. 8-8) $σφ=180πσp2p[degrees]$

Current best estimates for systematic uncertainties are 0.8% in percent polarization and 10° in polarization position angle.

# 8.2   Planning Observations

The HAWC instrument has two main observing configurations: Total Intensity Imaging and Polarization Imaging. The instrument also has two standard observing modes for imaging: the Nod Match Chop (NMC) mode combines traditional chopping with nodding and On the Fly Mapping (OTFMAP) mode keeps the secondary mirror fixed as the telescope primary is scanned across the source. The NMC observing mode is used for polarization observations; this mode includes chopping and nodding cycles in multiple half wave plate (HWP) positions.

The standard NMC mode is a subset of the standard two-position chopping with nodding mode (C2N). NMC consistis of several steps, listed below and illustrated in Figure 8-5.

1. Chop, where the secondary mirror of the telescope is moved at some frequency and angle.
2. Nod, where the telescope nods back and forth, each chopper beam being placed on the desired source.
3. Dither, which is a set of Nods at small offsets on the sky (nominally four positions), with each position having a Chop/Nod observation taken.
Figure 8-5.

Figure 8-5. The standard ABBA nod sequence of NMC mode.

Total Intensity observations with OTFMAP mode produce a continuous telescope motion with a two choices of pattern shape, the sizes of which are selected by the proposer. The first pattern (Box) is a series of linear scans used to map some rectangular region on the sky. The second pattern (Lissajous) is a curvilinear shape meant to cover a small region whose size is less than the array field of view.

## 8.2.1   Total Intensity Observations

### 8.2.1.1   On the Fly Mapping

In OTF mode, the secondary mirror remains stationary on the optical axis of the telescope while the telescope assembly itself slowly moves with respect to the sky. This scan motion modulates the celestial source with respect to the atmosphere in a manner similar to chopping the secondary mirror. Scan rates must reach (~2 Hz) x (HAWC+ beam width) in order to remove the source from the atmospheric background. This implies rates ~10–80 arcseconds per second depending on the bandpass.

In order to ensure absolute flux calibration in this mode, observers must carefully plan observations so that some of the mapped region contains no extended emission from the science target. Otherwise, one can only measure a differential flux with respect to the lowest measured intensity level. Further removal of residual atmospheric signal is performed by removing common-mode noise observed in all HAWC+ detectors. This averaging amounts to a spatial filter with size equal to the HAWC+ FOV. Therefore, while large maps may be necessary to reach a true zero-intensity level, users should be aware that one cannot also recover all spatial scales in a given region.

HAWC+ offers two scan types for OTFMAP scan patterns: Lissajous and Box. Lissajous scans are recommended for soucres smaller than the HAWC+ field of view (FOV) at a given bandpass, while Box scans (analogous to traditional raster scanning methods) are more efficient at mapping large areas several times the FOV. The patterns in Figure 8-6 show the two-dimensional location of the array center during the progression of a scan, with Lissajous scans depicted in the two top images and Box scans shown in the two bottom images. Two-dimensional scans are necessary in order to reconstruct all spatial scales in a map. The Lissajous scans are two-dimensional by definition, however Box scans require multiple scans, even in the case where a source fits completely in the HAWC+ FOV. The secondary (or cross) scan direction of a Box scan should by rotated with respect to the initial scan (orthogonal scans are best, although not absolutely necessary).

Figure 8-6.

Figure 8-6. Example scan patterns for HAWC+ OTFMAP mode. These patterns show the location of the central array pixel, which moves along the paths at a user-defined rate. The upper panels are Lissajous patterns. The top-left panel is shortly after starting an integration, while the top-right panel is after a longer time period. The lower-left panel shows a series of linear scans used to cover a larger region. The lower-right panel also shows the required cross-scan in the case of linearly scanned areas. Plots taken from Kovács (2008).

While proposers must request an area for scan mapping, they do not need to specify any specific pattern in Phase I proposals. Successful proposers will work with a SOFIA Support Scientist to choose an optimal scan pattern and strategy for their observations. For the purposes of the proposal, scan map time estimates should be made using the sensitivity estimates in Table 8-1. For sources smaller than the HAWC+ FOV, use the MDCF or NESB. For larger maps one may use the Mapping Speed.

Scan durations shorter than 10 min are recommended to ensure the stability of continuous OTFMAP observations for large periods of time. If a given map area and sensitivity cannot be achieved in that time, then multiple pointing positions should be used.

### 8.2.1.1a   Lissajous

In Lissajous observations, the telescope is driven to follow a parametric curve at a non-repeating period; as the scan progresses longer in time, more and more of the area defined by a scan amplitude will be covered. As commissioning of HAWC+ progresses, this sequence will be refined and may include additional calibration observations during the sequence described.

Figure 8-7 demonstrates the actual scan modes used in flight. The white box shows the Total Intensity FOV, the orange line shows the actual path as taken by the telescope, and the background images are the resulting image after the scan data is reduced.

Figure 8-7.

Figure 8-7.

### 8.2.1.1b   Box

In Box scans, the telescope is driven in a linear fashion at the specified rate in one direction for the given length and then moved perpendicularly before scanning in the reverse direction—similar to how one would mow a very large lawn. This is continued until the desired area is covered, after which the process repeats in the perpendicular direction to cross the same areas in the perpendicular direction.  For optimal reduction and coverage, three scans are performed, each at a slightly different starting angle to improve coverage and provide reduction robustness against systematic effects. As commissioning of HAWC+ progresses, this sequence will be refined and may include additional calibration observations during the sequence described.

Figures 8-8, 8-9, and 8-10 demonstrate the actual scan modes used in flight. The white box shows the Total Intensity field of view, the orange line shows the actual path as taken by the telescope, and the background images are the resulting image after the scan data is reduced.

Figure 8-8.

Figure 8-8. The scan starts at the bottom right, pauses midway through to obtain an estimate of tracking performance (the orange dot on the middle right) and then proceeds until the end.

Figure 8-9.

Figure 8-9. The scan starts at the upper right, pauses midway through to obtain an estimate of tracking performance (the orange dot on the middle of the top) and then proceeds until the end. The two directions are then combined to obtain the image below.

Figure 8-10.

Figure 8-10. The two directions from Fig.8-7 are then combined to obtain this image.

### 8.2.1.2   Nod Match Chop

In NMC mode, four dither points are created symmetrically about the central object coordinates; an example is given in Figure 8-11. At each dither position, chopping is started at the given throw and angle and the telescope is nodded between two symmetrically located points 180 degrees seperated from each other (positions A and B). As commissioning of HAWC+ progresses, this sequence will be refined and may include additional calibration observations during the sequence described.

NMC mode observations, are very time intensive and are subject to large observational overheads waiting for the telescope and/or secondary mirror assembly to complete chop/nod/dither movements. Estimated overheads before first flights were purposefully large (factors of 10!) and these large overhead factors remain in USPOT. As such, it is recommended that observers consider utilizing OTFMAP mode for Total Intensity observations, which provides better sensitivity and smaller overheads.

If the source has an angular extent larger than the HAWC+ FOV in NMC mode, or larger than can be accommodated in a 10 minute OTFMAP, the central position of each HAWC+ field must be specified, with due consideration of the desired overlap of the individual frames. For mosaic observations, proposers should ensure that they request the total integration time required for all fields.

Figure 8-11.

Figure 8-11. Example of a source being dithered between four positions. The green crosshairs give the position of one of the sources and is at the same physical location for each image, showing the image movement.

## 8.2.2   Polarimetry Observations

For Cycle 6, HAWC+ polarization observations may only be performed using the NMC observing mode. In this mode, four standard NMC observations are performed, one at each of four angles of the HWP (relative angles 0, 22.5, 45, and 67.5 degrees). This is followed by dithering, where the HWP cycle is repeated again for a total of four dither positions. We currently estimate an additional overhead of 90% efficiency associated with moving the HWP between positions. This has been incorporated into polarization sensitivities in Figure 8-3. The minimum time for a single polarization NMC observation with dithering is ~20 min.

As in the case of Total Intensity NMC, chopping into regions of bright, extended flux must be cafefully avoided. Additionally, the polarization state of that reference flux must be considered in both percent polarization and angle. Typically, neither of these values will be known for HAWC+ observations (although proposers may want to consult the latest Planck data release). This polarized reference beam will produce additional systematic uncertainties in the data. In the case where the source and reference beam have the same polarization level, the systematic polarization uncertainty is linearly proportional to the reference-to-source intensity ratio. For further discussion, see Schleuning et al. (1997) and Novak et al. (1997).

If the source has an angular extent larger than the HAWC+ FOV in NMC mode, the central position of each HAWC+ field must be specified, with due consideration of the desired overlap of the individual frames. For mosaic observations, proposers should ensure that they request the total integration time required for all fields.