7.1 Specifications
v7.1.3
Table of Contents

7.1 Specifications

7.1.1 Instrument Overview

7.1.1.1 Design


7.1.2 Performance

7.1.2.1 Filters


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7.1 Specifications
7.1.1 Instrument Overview
The Highresolution Airborne Wideband Camera (HAWC+) is a multiwavelength farinfrared imager and polarimeter with continuum bandpasses from 50 um to 240 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 Imaging Polarimetry, a rotating halfwave 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 diffractionlimited with a spatial resolution of 5 to 20 arcsec and a field of view (FOV) of ~2 to 10 arcmin. HAWC+ is currently not offering observations at 63 um (Band B).
7.1.1.1 Design
A schematic of the HAWC+ optical design is shown in Figure 71. Prior to entering the HAWC+ cryostat, light from the SOFIA telescope enters the set of warm foreoptics. 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 foreoptics, light enters the cryostat through a 7.6 cm diameter highdensity polyethylene (HDPE) window, then passing through a cold pupil on a rotatable carousel, a nearinfrared 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 72). The polarizing grid is heatsunk to the HAWC+ 1 Kelvin stage.
To perform polarimetry observations, a HWP matched to the bandpass 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 comounted 32x40 subarrays from NASA/GSFC and NIST. The detectors are superconducting transitionedge sensor (TES) thermometers on membranes with a wideband 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.
7.1.2 Performance
The absorbing coatings on the HAWC+ detector arrays were optimized to produce about 50% efficiency across the wide (50–240 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 71 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 71.
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 71). Total intensity observations are unaffected and can use the whole field of view via the R polarization state.
Parameter  Units  Band A  Band C  Band D  Band E 

Mean Wavelength (λ_{0})  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 Size^{a}  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 
NESB^{b} (photo)  MJy sr^{1} h^{1/2}  18.8  6.3  1.6  0.8 
MDCF^{c}  mJy  250  300  260  230 
Mapping Speed^{d}  See footnote ^{d}  0.0027  0.029  1.1  7 
MDCPF^{e}  % Jy  80  50  50  50 
IP^{f}  q  0.0154  0.0151  0.0028  0.0129 
u  0.0030  0.0090  0.0191  0.0111  
MIfP^{g}  MJy sr^{1} h^{1/2}  28,000  6,000  2,000  1,300 
Response Curve 
All photometric sensitivity estimates assume 100% observing efficiency without chopping and nodding. These values are preflight estimates and subject to change after the HAWC+ instrument has been commissioned. SITE provides the onsource time for specific observations, while USPOT estimates the overhead for a given instrument configuration.
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.
7.1.2.1 Filters
HAWC+ can produce images using continuum bandpasses in either Total Intensity Imaging or Imaging Polarimetry configurations. In Imaging Polarimetry, the dualbeam 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 Imaging Polarimetry, 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 the four available filters. Figure 73 shows transmission profiles including all filters for all bandpasses. The effective wavelengths and bandwidths averaged over the total filter transmission are given in Table 71.
7.1.2.2 Total Intensity Imaging Sensitivities
The equations provided below are included for informational purposes only, and should not be entered into USPOT. Integration times calculated using the equations below include overheads, and USPOT already adds the telescope overheads into the exposure times entered. For USPOT entries use SITE, which only takes into account onsource time.
Observations with HAWC+ for measurements of Total Intensity can be performed using either onthefly 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 twoposition chop, parallel to the nod direction where the chop amplitude matches the nod amplitude (NMC).
Table 71 presents 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 onehour 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 onsource integration time.
(Eq. 71) $$t={\left(\frac{\mathrm{NESB}}{\sigma}\right)}^{2}$$
(Eq. 72) $$t=\left(\mathrm{900\; s}\right){\left(\frac{\mathrm{NESB}}{\sigma}\right)}^{2}$$
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 73:
(Eq. 73) $$M=\frac{d\Omega}{\mathrm{dt}}=\frac{{\mathrm{\gamma \Omega}}_{\mathrm{array}}}{{s}^{2}}$$
where γ is related to the filling factor, Ω_{array} 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 71 are given for S/N = 1 in a onehour integration time assuming γ = 1, while SITE and Figure 73 use a more realistic value γ = 0.75. The time to map an area Ω (≥ Ω_{array}) to a sensitivity level σ is given by Equation 74:
(Eq. 74) $$t=\frac{{\Omega}_{}}{M{\sigma}^{2}}$$
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 71 and Figure 73 we use a precipitable water vapor of 7.3 μm, a 50° zenith angle, and a telescope emissivity of 15%.
7.1.2.3 Imaging Polarimetry Sensitivities
The equations provided below are included for informational purposes only, and should not be entered into USPOT. Integration times calculated using the equations below include overheads, and USPOT already adds the telescope overheads into the exposure times entered. For USPOT entries use SITE, which only takes into account onsource time.
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 preflight 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 σ_{p} follows from the imaging sensitivity σ_{I} so that Equation 75 is true:
(Eq. 75) $${\sigma}_{P}=\frac{{\sigma}_{I}\sqrt{2}}{{\eta}_{p}I}$$
where I is the source intensity, η_{p} is the system polarization efficiency, and σ_{p} is measured in units of percent (%). The Minimum Detectable Continuum Polarized Flux (MDCPF) reported in Table 71 is the value σ_{p} x I above, and follows from the total intensity MDCF. USPOT will add overhead values appropriate to NMC mode for polarimetry.
For Imaging Polarimetry, 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 σ_{p} = 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 71 lists these values for a onehour integration time in units of surface brightness for an extended source where, unlike other values in Table 71, all appropriate overhead values have been added.
HAWC+ time estimates should be made using the online exposure time calculator, SITE. Note that integration times scale as shown in Equation 76 and Equation 77 from the values in Table 71:
(Eq. 76) $$t=\mathrm{(1\; h)}{\left(\frac{\mathrm{MIfP}}{I}\right)}^{2}{\left(\frac{\mathrm{0.3\%}}{{\sigma}_{p}}\right)}^{2}$$
(Eq. 77) $$t=\mathrm{(900\; s)}{\left(\frac{\mathrm{MDCPF}}{4{\sigma}_{p}I}\right)}^{2}$$
where t is the integration time and σ_{p} 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 78:
(Eq. 78) $${\sigma}_{\phi}=\frac{180}{\pi}\frac{{\sigma}_{p}}{2p}\mathrm{[degrees]}$$
Current best estimates for systematic uncertainties are 0.8% in percent polarization and 10° in polarization position angle.