10.1 Instrument Overview

10.1.1 Design

A schematic of the HAWC+ optical design is shown in Figure 10-1. Light enters the set of warm fore-optics mounted outside the cryostat, reflecting from a folding mirror and a field mirror that images the SOFIA pupil at the cold pupil inside the HAWC cryostat. After the fore-optics, light enters the cryostat through a 7.6 cm (3.0 in) diameter high-density polyethylene (HDPE) window, followed by near-infrared blocking filters to define each bandpass and lenses designed to optimize the plate scale, then the cold pupil on a rotatable carousel. The pupil 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.

The pupil carousel and filter/lens wheel are at an approximate temperature of 10 K; after this point the light passes through a wire grid that reflects one component of linear polarization and transmits the orthogonal component. The grid directs the two components (often referred to as the R and T components) to the two detector arrays and the grid itself is heat-sunk to the HAWC+ 1 Kelvin stage

In the case of polarimetry, the half-wave plate (HWP) matched to the band-pass is selected and rotated to modulate the incident polarization states.  Alternatively, unpolarized intensity can be measured without polarization by removing the HWPs from the optical path (utilizing the open pupil position) and simply summing the polarization states.

While HAWC+ is designed for two 64x40 detector arrays, one full array (for R) and one half array (for T) are currently installed.  The 64x40 HAWC+ detector arrays 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 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 a base temperature of ~0.1- 0.2 K.

Schematic of the HAWC+ optics

Figure 10-1: 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.

10.1.2 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 included 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, confirming that the system should be diffraction limited on SOFIA. Initial analysis of the first commissioning data from May 2016 show that this is approximately the case, though final data reduction and accompanying analysis is pending.  Table 10-1 lists the FWHM of Gaussian beams approximating the SOFIA/HAWC+ beams, taking into account the monochromatic diffraction limit, the finite size of the HAWC detectors, and a convolution across the measured filter bandpasses. The filter transmission curves (text tables) are available as a zip file or individually from Table 10-1.

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 detector's X direction (the first element of the Field of View in Table 10-1).  Total intensity observations are unaffected and can use the whole field of view via the R polarization state.

Table 10-1: HAWC+ Instrument Characteristics

HAWC+ Instrument Characteristics
Parameter Units Band A Band B Band C Band D Band E
Mean Wavelength (λ0) μm 53 63 89 154 214
Filter Width (Δλ/λ0) - 0.17 0.15 0.19 0.22 0.20
Resolution (FWHM) arcsec 4.7 5.8 7.8 14 19
Pixel Pitchf arcsec 2.6 4.0 4.0 6.8 9.1
Field of View arcmin 2.7x1.7 4.2x2.6 4.2x2.6 7.3x4.5 8.0x6.1
NESBa (photo) MJy sr-1 h1/2 15 12 4.7 1.2 0.57
MDCFb mJy 69 85 60 47 43
Mapping Speedc See footnote c 0.016 0.059 0.39 18 110
MDCPFd % Jy 11 13 9.5 7.3 6.7
MIfPe MJy sr-1 h1/2 24,000 20,000 7700 1900 940
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Note: 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 SPT time calculator will estimate the correct overhead values for C2N.

a Noise Equivalent Surface Brightness for S/N = 1 into a single HAWC+ beam (FWHM given here).

b Minimum Detectable Continuum Flux for a point source with S/N = 4 in a 900 second integration.

c Real scan rate required to achieve a given an NESB. Units: arcmin2 h-1 (MJy sr-1)-2

d Minimum Detectable Continuum Polarized Flux for a point source with a S/N = 4 in a 900 second integration. eMinimum 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.

f 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.

10.1.3 Filters

Imaging with HAWC+ can be performed in either TOTAL INTENSITY or POLARIZED INTENSITY modes. The dual-beam nature of HAWC+ allows simultaneous measurement of both total and unpolarized intensity (Stokes parameters I, Q, and U) in the POLARIZED mode since the total intensity is given simply by the sum of the signal in the two polarization beams (neglecting circular polarization). The HWPs that allow modulation of the polarization can also be removed from the optical path such that the beam passes through an open pupil for TOTAL mode. There is a slight gain in total sensitivity in this mode 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 optical filters. Each passband includes a bandpass filter and a number of low-pass cut-off filters. Figure 10-2 shows transmission profiles including all filters for all bandpasses. The effective wavelengths and bandwidths averaged over the total filter transmission are given in Table 10-1.

HAWC+ filter transmission profiles

Figure 10-2: HAWC+ filter transmission profiles.

10.1.4 Imaging Sensitivities

Observations with HAWC+ for measurements of total (unpolarized) intensity can be performed using either on-the- fly scanning (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 former mode is the far more efficient mode, but has not yet been tested by other imaging instruments on SOFIA. The chopping option consists only of a two-position chop, parallel to the nod direction where the chop amplitude matches the nod amplitude (C2N-NMC).

Figure 10-3 and Table 10-1 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 10-3 plots the MDCF for both observing modes OTFMAP and C2N (NMC) where the latter follows from the former based on overheads related to chopping and nodding the telescope.

HAWC+ sensitivity

Figure 10-3: 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 10-1 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 polarization, the plotted data show the polarized intensity p x I, where p is the fractional polarization (not percent).

HAWC time estimates should be made using the on-line exposure time calculator, SITE. Here we note that integration times scale in the following manner from the values in Table 10-1:




where t is the integration time and σ is the desired sensitivity for S/N = 1, each in the appropriate units. For OTF mapping, a useful sensitivity value is the mapping speed


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 10-1 are given for S/N = 1 in a one-hour integration time assuming γ = 1, while SITE and Figure 10-3 use a more realistic value γ = 0.75. The time to map an area Ω (≥ Ωarray) to a sensitivity level σ is given by


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 10-1 and Figure 10-3 we use a precipitable water vapor of 7.3 μm, a 50° zenith angle, and a telescope emissivity of 15%.

10.1.5 Polarization 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


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 10-1 is the value σp x I above, and follows from the unpolarized MDCF. SPT will add overhead values appropriate to C2N mode for polarimetry.

For polarization imaging another useful quantity is the Minimum unpolarized 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 10-1 lists these values for a one-hour integration time in units of surface brightness for an extended source where, unlike other values in Table 10-1, all appropriate overhead values have been added.

HAWC+ time estimates should be made using the on-line exposure time calculator, SITE. Here we note that integration times scale in the following manner from the values in Table 10-1:




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:


The above values assume only statistical uncertainties. Current best estimates for systematic uncertainties are no better than 0.3% in percent polarization and 2° in polarization position angle.