# 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.
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.