Setting requirements on out-of-band rejection for next-generation CMB experiments. Application to the LiteBIRD instrument

Technical Summary: Setting Requirements on Out-of-Band Rejection for Next-Generation CMB Experiments

Problem Statement
Next-generation Cosmic Microwave Background (CMB) experiments, such as LiteBIRD, aim to measure the B-mode polarization signal to constrain the tensor-to-scalar ratio ($r$) with a precision of $\delta r < 0.001$. Achieving this requires not only high sensitivity but also unprecedented control of instrumental systematic effects. A critical challenge is the rejection of "out-of-band" power—radiation at frequencies outside the telescope's designed passband. This out-of-band power originates from astrophysical foregrounds (e.g., Galactic dust, synchrotron, zodiacal light) and the instrument's own thermal emission. If not sufficiently attenuated, this power can degrade detector performance, increase thermal loads, and bias the separation of astrophysical components, thereby compromising the measurement of primordial gravitational waves.

Methodology
The authors developed a comprehensive methodology to derive quantitative requirements for out-of-band rejection levels, specifically applied to the Medium- and High-Frequency Telescopes (MFT and HFT) of the LiteBIRD mission. The approach involves:

1. Frequency Domain Definition: The spectrum is divided into five domains: Telescope In-Band (TIB), Detector In-Band (DIB), Low Out-of-Band (LOB), Complementary Out-of-Band (COB), and High Out-of-Band (HOB).
2. Modeling:
   • Sky Modeling: Spectral radiance for five components (CMB, Galactic dust, synchrotron, interplanetary dust, and OB stars) is modeled using Planck laws and modified black-body/power-law distributions, scaled to maximum observed intensities to ensure conservative estimates.
   • Instrument Modeling: A refractive optical design is assumed, including a Half-Wave Plate (HWP), two lenses (L1, L2), and a focal plane. The optical response and thermal emission of these components are modeled across the 1–106 GHz range, with specific emissivity models derived for polypropylene (HWP) and polyethylene (lenses) based on laboratory data.
3. Power Propagation: The total power received by a detector is calculated by integrating the incident spectral density over the frequency domains, weighted by the instrument's transfer function and attenuation factors ($A^d_i$) at various filter positions ($s$) along the optical path.
4. Analysis Types:
   • Static Analysis: Evaluates the impact of constant out-of-band power on detector Noise Equivalent Power (NEP), component separation efficiency (bias on $r$), and the static thermal heat load on optical elements and the focal plane.
   • Dynamic Analysis: Assesses the impact of temporal fluctuations in out-of-band power (due to sky scanning and instrument thermal variations) on NEP stability and temperature stability of the focal plane and optical elements.

Key Contributions and Results
The study derives specific attenuation requirements (in dB) for the LOB, COB, and HOB domains across the 10 frequency channels of the MFT and HFT. The results are summarized as follows:

• Dominant Constraints: The most stringent requirements arise from the static analysis of the detection chain, specifically regarding detector NEP performance and component separation efficiency.
  • NEP Performance: To limit the increase in detector NEP to $\Delta \text{NEP} \le 0.14 \, \text{aW}/\sqrt{\text{Hz}}$, the HOB domain requires attenuation factors ($A_H$) ranging from 58 to 82 dB, depending on the frequency channel. The LOB and COB requirements are generally lower (e.g., $A_L \approx 15-28$ dB, $A_C \approx 18-46$ dB).
  • Component Separation: To keep the bias on the tensor-to-scalar ratio ($r$) within the allocated budget ($6.5 \times 10^{-6}$), requirements are slightly less stringent than NEP constraints but still significant, with $A_H$ requirements ranging from 60 to 69 dB.
• Thermal Constraints: The impact of out-of-band power on the thermal cooling budget is found to be much less stringent than detection chain constraints.
  • The heat load on the focal plane from out-of-band radiation is a small fraction of the total cooling budget.
  • The heat load on the HWP is negligible compared to the power dissipated by eddy currents.
  • The heat load on the lenses is well within the available cooling power at the 4.8 K stage.
• Dynamic Constraints: Requirements derived from dynamic stability (fluctuations in NEP and temperature) are very loose compared to static requirements. The long thermal time constants of the optical elements (approx. 30 hours for the HWP, 10 hours for lenses) and the modulation by the rotating HWP effectively filter out low-frequency sky variations.
• Filter Placement: The analysis suggests that for thermal load constraints, the most critical filter position is $s_1$ (between the second lens and the focal plane), as this is where the majority of the HOB heat load from the HWP and tube enters the focal plane. However, for NEP and component separation, the requirement applies to the total attenuation across all filter positions.

Significance and Claims
The paper claims to provide a general, rigorous methodology for translating high-level scientific and instrumental requirements into specific engineering specifications for out-of-band filtering. The primary significance lies in establishing that detection chain performance (NEP and component separation) drives the filtering requirements, rather than thermal constraints, which are often a concern in cryogenic instrument design.

The authors state that the derived requirements (particularly the high attenuation needed in the HOB) will serve as input specifications for designing the telescope filtering scheme for LiteBIRD. They note that while the specific design may evolve, the methodology presented is robust and applicable to other current and future CMB experiments. The work also supports the preparation of calibration tests for the instrument prior to launch. The study concludes that while dynamic effects are negligible due to the instrument's thermal inertia and modulation strategy, the static rejection of out-of-band power is critical for achieving the mission's scientific goals.