Optical concept model of the future cosmology project BISOU

We present an optical analysis of BISOU (Balloon Interferometer for Spectral Observations of the primordial Universe), an astronomical balloon-borne pathfinder spectrometer developed as part of a preparatory study for a future space mission aiming at measuring spectral distortions of the cosmic microwave background (CMB). The BISOU optical system is based on a differential polarising Fourier Transform Spectrometer (FTS) that receives inputs from both a sky-facing telescope and an internal calibration source. The FTS focal planes are equipped with bolometric detectors coupled to multimode feed horns, with distinct focal planes dedicated to the low (90 - 300 GHz) and high (0.3 - 1.5 THz) frequency bands. The optical analysis first relies on ray-tracing simulations to establish the overall configuration of the system, before proceeding to more advanced Gaussian beam and physical optics analyses.

The design of the BISOU instrument is inspired by the PIXIE proposal, but it has been adapted to meet the constraints of a balloon-borne experiment rather than those of a space mission. The instrument is a differential Fourier Transform Spectrometer (FTS) based on a polarised Martin–Puplett interferometer with two inputs: one arm observes the sky, while the other is looking at an internal blackbody reference maintained at the temperature of the CMB (2.7 K). The FTS output, where detectors are located, collects a signal consisting of a constant part and a FTS scan-modulated part proportional to the difference between the two inputs. The beams are split and recombined using wire-grid polarisers, and an optical path difference is introduced by a pair of moving mirrors. The outputs of the FTS are coupled to detectors with multimode feedhorns. The accurate reference is essential for spectral distortion measurements, as the signal corresponds to tiny deviations from an almost perfect blackbody spectrum. Without a well-characterized calibrator, systematic effect will limit the ultimate sensitivity.

As the instrument is designed for a balloon mission, it faces additional challenges compared to a traditional space mission. This is mainly due to the residual atmosphere that is still present at an altitude of 40 km (P = 3 mbar). In order to achieve the required sensitivity, the instrument will be maintained at 2.7 K, while the focal plane will be cooled to a few hundred millikelvin in order to reach the operating temperature of the detectors. Therefore, the presence of the atmosphere necessitates the instrument being enclosed in a cryostat capable of withstanding the pressure difference between the external environment and the internal vacuum. The photon noise is dominated by the thermal emission of the residual atmosphere and the warm optical component (270 K) such as the window and filters. While the window is transparent to millimiter and submillimeter waves and is here to close the cryostat, the filters limit the thermal load on each temperature stage of the instrument. All these optical components must be carefully characterised in order to separate and subtract their contributions from the measured signal.

To improve the sensitivity of the instrument, the wide frequency band is subdivided using a dichroic filter. Frequencies below the cut-off frequency (300 GHz) are transmitted through the dichroic, while higher frequencies are reflected by its surface. Separating frequencies into two sub-bands significantly reduces the power received by the detectors and, consequently, the photon noise in the low-frequency band. This is particularly advantageous for a balloon-borne mission, where high-frequency emissions are largely caused by the internal emission of warm instrument components. This reduction in photon noise improves the sensitivity and overall performance of the instrument, particularly in the low-frequency channel.

The instrument’s key mechanism relies on a pair of moving mirrors, the displacement of which is directly linked to the instrument’s specifications. The maximum optical path difference (OPD) between the two arms determines the instrument’s spectral resolution, which is set to ∆ν = 15 GHz according to equation 1. Furthermore, the optical path difference spacing δ between two measurement points in the interferogram relates to the maximum frequency of the BISOU broadband signal, as described by equation 2. As the mirrors are displaced from their nominal positions by a distance z through the FTS mechanism, an additional optical path length of approximately 2z is introduced in one arm, while the path length in the other arm is reduced by the same amount. This results in an optical path difference of approximately δ = 4z. Further investigation using ray-tracing simulations is required to establish a more accurate and comprehensive relationship between mirror displacement and the actual optical path difference. With BISOU’s spectral resolution of ∆ν = 15 GHz, we require a maximum optical path difference of 2 cm, which corresponds to a total mirror stroke of ± 2.5 mm. In this paper, we explored the case of a mirror stroke of ± 10 mm, corresponding to four times the stroke required to reach our target sensitivity.

A cryogenic Breadboard model (BBm) is being built at the Institut d’Astrophysique Spatiale (IAS). This cryogenic prototype represents an important step toward validating the concept, studying systematic effects that are still unknown for this type of instrument, and testing new technologies such as detectors. In particular, the asymmetry of the two optical paths will need to be studied.

The initial optical design of the instrument was carried out using ray-tracing in the industry-standard Zemax OpticStudio and GRASP software. The more detailed analyses, especially at the lower operating frequencies where the beam is the largest (νmin = 90 GHz or λmax = 3.3 mm), were carried out using full vector physical optics in GRASP. The beam is well-modelled by rays at the high-frequency end of the band.

The initial optical design of the current version of our instrument was based on geometrical optics (GO). This approximation is valid when rays are considered infinitely thin, the light source is point-like, and optical surfaces are ideal (with a reflection coefficient of 1). Ray tracing is particularly useful for multi-wavelength instruments, as the behavior of rays is independent of wavelength due to the achromatic nature of our reflective optics. This approximation allowed us to quickly and easily model light propagation through the instrument, thanks to the Zemax software. It helped us select the most suitable mirror types for our needs, to ensure the beam passes through specific optical elements. In our BISOU design, the last FTS mirror M5 has been changed from an elliptical mirror, used in PIXIE design, to a parabolic mirror. This produces a collimated beam on the dichroic, ensuring that all incident rays reach it at the same angle of incidence, which simplifies the characterization of this critical component. The mirror M6 is now used to focus the beam onto the feedhorns. To achieve the detectors’ operating temperature of a few hundred millikelvin, the detectors and their associated feedhorns must be co-located within the same area.

One of the most important constraints for the BISOU mission is related to its balloon-based platform. The instrument needs to fit in a standard gondola (CARMEN - CNES), the lift resulting from a 800 000 m3 He balloon. The BISOU FTS design (mirrors M1 to M5), has been simplified to a five-mirror configuration compared to the six-mirror design used in instruments such as PIXIE original design. The mirror M1 directly images the internal reference, thereby avoiding the need for a complex and heavy optical path to inject the reference signal into the FTS arm. This reduction in the number of optical elements enables a decrease in the overall mass of the FTS while preserving the same interferometric signal formulation at the detector level. We have chosen a telescope following the Mizugushi-Dragone (MD) condition, in its Gregorian version, in order to minimize the cross-polarisation and the astigmatism of the system. Its output had to be modified to be used as input of the interferometer to illuminate the first of the five concave mirrors. To avoid any risk of field of view vignetting by the balloon we considered a limiting elevation angle of 50° compared to the plane of the FTS horizontal plane. This constraint is added to the MD condition and complexifies the design of the telescope.

In the millimetre-wave domain, Gaussian optics is preferred to the usual GO approach when the size of the system (mirrors, aperture,...) is comparable to the wavelength (few mm). In this regime, the effects of diffraction, the beam divergence or the phase curvature become critical and are not modelled by straight rays. Even if BISOU will operate with multimoded horn, the first modelling is performed by considering them as monomode gaussian beams. Gaussian optics allows to model the size of the beam quickly and its behaviour across the instrument, which is critical in order to determine the size of the instrument and begin to optimise the optical system and the overall design. In our first modelling, we consider that the beam is a gaussian, entirely described by two parameters, the frequency ν and the size of the waist ω0. The waist of a gaussian beam is its minimum beam radius, corresponding to the region where the wavefront is nearly planar and the phase most uniform. It defines the effective size of the equivalent Gaussian source and sets the beam’s divergence during propagation. As an approximate starting point typical at those frequencies, we set our feed’s waist at 9 mm at 90 GHz. All further modelling is performed at 90 GHz, the lowest frequency in the BISOU frequency range, where the beam is the widest.

Thanks to this gaussian feed, we have a simple analytical way to compute the size of the beam at each optical element without running a simulation. We aim at a edge taper of-35 dB for each edge of the mirror in the FTS in order to limit spillover and guarantee that the useful field remains compatible with the detector’s field of view. Such a level of edge attenuation ensures that 98% of the beam power is contained inside the envelope of the beam, strongly reducing diffracted contributions that could degrade the instrument’s response. This choice must, however, be interpreted in light of the horn transmitter/receiver convention: the pattern used to describe the mirror illumination actually corresponds to the horn’s radiation pattern in transmission, which is identical to its reception response by electromagnetic reciprocity. However on the main reflector we aim for a edge taper of-20 dB to lighten the design constraints and keep a reasonably sized primary mirror. The gaussian beam is an effective way to adjust mirror parameters (reflection angles, focal distance...) in order to reach the target illumination on each of the optical elements. This optimization allowed us to reduce the size of mirrors M2 and M4 compared to the other mirrors of the FTS. While the largest FTS mirror have a side length of 90 mm, we were able to decrease the side length of the smaller mirrors to 70 mm without increasing the spillover.

We used GRASP to study how displacements of the moving mirror change the mirrors illumination and impact the instrument’s performance. In particular, we examined the instrument’s spillover at the extreme mirror positions, as well as any beam deformation throughout the optical system. We computed the spillover throughout the optical system using the standard antenna emission/receiving convention. By shifting the moving mirror to its extreme position, we can analyze the power radiated by the feedhorns that falls outside the optical elements. In this paper, we considered a maximum mirror stroke of ± 10 mm, which exceeds the displacement likely to be used on BISOU. In the reception convention, this lost power corresponds to undesirable radiation that the feedhorn would see from external elements along the optical path. This approach allows us to quantify the efficiency and identify potential sources of stray light at each stage of the system. This simulations were performed using gaussian beams. This approach was chosen because the gaussian beam is a predefined source model available in Ticra GRASP, and is thus easy to configure and implement. It also allows for fast computations at each frequency, which is particularly advantageous for the preliminary analyses. This initial modelling provides a good way to estimate the changes in the beam when the moving mirror is displaced.

Thanks to our preliminary design using the analytic Gaussian beam with the –35 dB envelope, we keep the power loss through the FTS (feed to M1) below 0.2% at 90 GHz when the moving mirror is in its nominal position. The total power lost through the system (FTS + telescope) remains below 7.5%. We also calculated the power lost through the optical system when the moving mirrors M3 were moved to their extreme positions (± 10 mm). Due to the-20 dB edge taper requirement on the sides of the telescope’s primary mirror, displacement of the mirror and the difference between the original and modified optical paths does not dramatically affect the spillover of the instrument and the loss stay around 10%. We note, however, an asymmetry between the optical paths at +10 mm and-10 mm mirror stroke, likely due to the mirror shapes. This asymmetry will need to be investigated more thoroughly in future simulations. Nevertheless, the results presented here correspond to a resolution four times higher than the one required for BISOU, with a mirror stroke four times larger than needed. These results are therefore very encouraging for future developments.

When the moving mirrors are displaced, the rays no longer strike the centres of the mirrors, which can introduce optical aberrations. To verify that these aberrations remain acceptable, we use a Gaussian beam to simulate the system and assess how the beam shape changes as the mirror moves. This ensures that the optical performance of the instrument is maintained throughout the full range of mirror displacement. Results of the simulations show that the beam remains essentially aligned along the same horizontal axis, with minimal variation in the vertical axis. Depointing remain below ± 0.1°. In addition, the overall gaussian shape of the beam is preserved as well as the directivity. The maximum directivity loss between the nominal position and + 10 mm remains limited to 0.5 dB. This indicates that the pointing stability of the system is very robust to mirror movements within the considered range.

In this paper, we have described the different approaches used in the design of the BISOU instrument. The ray tracing and gaussian beam approaches were employed to accommodate the constraints associated with the balloon-based nature of the mission while taking the beam width into account. This design enabled us to compute the beam through the optical system and estimate the effect of the movement of the moving mirror on the projected beam. In future work, we will model the behaviour of the multimode horn throughout the system and compute a more realistic beam pattern. In addition, a breadboard model of the instrument being constructed at IAS before the end of the year will enable us to perform the first measurements and compare them with our model.

Improvements to AI Systems Based on This Paper:

1. AI for Multi-Regime Optical Simulation Selection

• Improvement: Train an AI model to automatically choose between ray tracing, Gaussian beam, and physical optics based on frequency, component size, and wavelength ratio (e.g., when λ > 1/10 of mirror aperture, switch from GO to Gaussian).

• Capability: The AI can design optical systems for balloon/space instruments by predicting which approximation is valid at each stage, reducing manual iteration time and errors.

2. AI-Driven Tolerance and Asymmetry Analysis

• Improvement: Use machine learning to map mirror displacement (e.g., ±10 mm) to beam deformation, spillover, and pointing shifts, learning from GRASP simulations to predict performance without running full physical optics each time.

• Capability: The AI can rapidly evaluate thousands of mechanical tolerance scenarios, flagging asymmetric path losses (as seen between +10 mm and-10 mm) and suggesting mirror shape adjustments to minimize systematic errors.

3. AI-Optimized Edge Taper Allocation

• Improvement: Implement a reinforcement learning agent that optimizes edge taper values (e.g., -35 dB for FTS mirrors, -20 dB for primary reflector) across all optical elements to minimize total power loss while balancing mirror size and stray light constraints.

• Capability: The AI can automatically generate compact, high-efficiency optical layouts for multimode feedhorn systems, reducing spillover below 0.2% in FTS and 7.5% overall, as achieved in this paper, but for arbitrary frequency bands.

4. AI for Dichroic Filter Design and Band-Splitting Optimization

• Improvement: Train a neural network to predict photon noise reduction and sensitivity gains from dichroic cut-off frequencies, given atmospheric emission models and instrument temperature stages.

• Capability: The AI can recommend optimal sub-band splits (e.g., 90-300 GHz vs. 0.3-1.5 THz) for balloon missions, balancing detector thermal load and signal-to-noise ratio, and can auto-design the dichroic surface to minimize in-band losses.

5. AI-Powered Calibration and Systematic Effect Separation

• Improvement: Develop a Bayesian inference AI that separates contributions from residual atmosphere, warm windows, and filters from the measured interferogram, using prior models of each component’s spectral response.

• Capability: The AI can autonomously calibrate the instrument in-flight, subtracting atmospheric and warm-component emission to achieve the required sensitivity for CMB spectral distortion measurements, even with imperfect component characterization.

6. AI for Cryostat and Thermal-Optical Co-Design

• Improvement: Use a generative AI to co-optimize cryostat window thickness, filter stages, and mirror geometries to minimize thermal loading while maintaining beam quality (e.g., keeping beam waist within feedhorn constraints).

• Capability: The AI can propose novel window/filter configurations that reduce photon noise from 270 K components, potentially improving low-frequency sensitivity beyond current designs.

7. AI for Multimode Feedhorn Modeling

• Improvement: Train a surrogate model (e.g., a deep learning emulator) on physical optics simulations of multimode horns to predict beam patterns and coupling efficiencies across frequency and horn geometry.

• Capability: The AI can replace the current single-mode Gaussian approximation with realistic multimode behavior, enabling accurate end-to-end system simulations for instruments like BISOU without heavy computational cost.

8. AI for Automated Mirror Stroke Optimization

• Improvement: Apply an optimization algorithm (e.g., Bayesian optimization) to find the minimum mirror stroke that meets spectral resolution (Δν = 15 GHz) while maintaining spillover below 10% and directivity loss < 0.5 dB.

• Capability: The AI can reduce mechanical stroke requirements (e.g., from ±10 mm to ±2.5 mm) while preserving performance, leading to lighter, more reliable mechanisms for balloon payloads.

9. AI for Asymmetric Path Compensation

• Improvement: Use a neural network to learn the asymmetry in optical path differences (as observed between +10 mm and-10 mm strokes) and predict correction factors for interferogram processing.

• Capability: The AI can automatically correct for systematic phase and amplitude errors introduced by mirror displacement, improving spectral fidelity without redesigning the optics.

10. AI for End-to-End Mission Performance Prediction

• Improvement: Build a digital twin AI that integrates ray tracing, Gaussian beam, physical optics, thermal models, and detector noise to predict the final sensitivity of BISOU-like instruments under varying atmospheric conditions (e.g., 3 mbar at 40 km altitude).

• Capability: The AI can simulate the entire instrument lifecycle—from design to flight—allowing engineers to test what-if scenarios (e.g., changing elevation angle limits, window emissivity) and optimize the mission before building hardware.

We present an optical analysis of BISOU (Balloon Interferometer for Spectral Observations of the primordial Universe), an astronomical balloon-borne pathfinder spectrometer developed as part of a preparatory study for a future space mission aiming at measuring spectral distortions of the cosmic microwave background (CMB). The BISOU optical system is based on a differential polarizing Fourier Transform Spectrometer (FTS) that receives inputs from both a sky-facing telescope and an internal calibration source. The FTS focal planes are equipped with bolometric detectors coupled to multimode feed horns, with distinct focal planes dedicated to the low (90 - 300GHz) and high (0.3 - 1.5THz) frequency bands. The optical analysis first relies on ray-tracing simulations to establish the overall configuration of the system, before proceeding to more advanced Gaussian beam and physical optics analyses.