The next generation of far-infrared space observatories must be cryogenically cooled to fully exploit the sensitivity of state-of-the art detectors. It is widely accepted that a Fourier transform spectrometer (FTS) is the optimum solution for high-resolution spectroscopy. The FTS itself requires precision, low-power, and robust cryogenic displacement metrology; previous missions have used capacitive, inductive, and optical encoder displacement metrology systems, however, to date, no mission has flown a cryogenic range-resolved laser interferometer for such a purpose. Interferometers confer advantages of high precision and low thermal power dissipation that can meet the stringent requirements of future missions. We have developed a cryogenic, multiaxis, range-resolved laser interferometer based on sinusoidal frequency modulation (SFM) that requires only a single laser and a single photodetector to simultaneously measure up to eight axes. We present the theory, key design considerations, calibration methods, and application of the SFM technique to simultaneous multiaxis measurements under both ambient and cryogenic conditions. To the best of our knowledge, the latter represents, for the first time, simultaneous cryogenic multiaxis displacement measurements using a probing beam launched within the cryogenic workspace.

The PRobe far-Infrared Mission for Astrophysics (PRIMA) will feature a 1.8 m cryogenically cooled telescope that will enable astronomical spectroscopy at both low-resolution and high-resolution over a broad spectral range. In the absence of telescope self-emission and with access to ultra-sensitive detectors, the point source sensitivity of a broad spectral observation is limited by photon noise. The only meaningful way to reduce photon noise is by restricting the instantaneous spectral bandwidth observed by a single detector, typically to a fraction of one percent. In the case of the Far-InfraRed Enhanced Survey Spectrometer (FIRESS) instrument, low-resolution spectroscopy is achieved using several reflection diffraction gratings to restrict the spectral bandwidth. For high-resolution spectroscopy, a Fourier transform spectrometer is placed in front of and in series with the grating spectrometer, which serves as a post-dispersing element to achieve the same goal. The polarization encoding properties of a Martin-Puplett interferometer can exploit the strong polarization dependence of the low-resolution diffraction grating, by ensuring the interferometer output presents the transverse magnetic polarization mode to the grating. We term this hybrid instrument the post-dispersed polarizing Fourier transform spectrometer (PDPFTS). A fully cryogenic far-infrared PDPFTS has been developed in our laboratory to gain a better understanding of the challenges presented by this instrument. The results we present will help to guide the development of FIRESS. (c) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License.

There is a growing need for low power, precision metrology in spaced-based cryogenic environments. Displacement sensors used in previous space astronomy missions have included capacitive, inductive, and optical encoders, however, the need to reduce the power dissipation in the cryogenic workspace has driven a transition towards laser-based solutions. Our previous research has explored several range-resolved laser interferometry techniques suitable for cryogenic applications. Most recently, we have developed a frequency-modulated continuous-wave (FMCW) multi-axis laser interferometer based on the method of sinusoidal frequency modulation (SFM). This system has demonstrated, to the best of our knowledge, the first fully cryogenic (<4 K), simultaneous, multiaxis displacement measurements using a single laser and detector. While the SFM technique has not yet been implemented on a cryogenic space-based platform, it is the leading candidate for displacement metrology on the NASA PRIMA mission. In the SFM technique, the optical frequency of the laser undergoes sinusoidal modulation about a central frequency. Any deviation of the central frequency from its assumed value introduces an error in the measured displacement. This paper introduces a novel concept for frequency stabilization of FMCW systems in which the central optical frequency is locked onto a molecular absorption line to provide a stability of 0.1pm in wavelength. Preliminary results obtained using this calibration method in the context of SFM range-resolved laser interferometry are presented.

Recent advances in far-infrared detector technology have led to increases in raw sensitivity of more than an order of magnitude over previous state-of-the-art detectors. With such sensitivity, photon noise becomes the dominant noise component, even when using cryogenically cooled optics, unless a method of restricting the spectral bandpass is employed. The leading instrument concept features reflecting diffraction gratings, which post-disperse the light that has been modulated by a polarizing Fourier transform spectrometer (FTS) onto a detector array, thereby reducing the photon noise on each detector. This paper discusses the development of a cryogenic (4 K) diffraction grating spectrometer that operates over the wavelength range of 285 to 500 μm and was used to post-disperse the output from a room-temperature polarizing FTS. Measurements of the grating spectral response and diffraction efficiency are presented as a function of both wavelength and polarization to characterize the instrumental performance.

Double-Fourier interferometry (DFI) from a space-based platform provides a path to achieve broadband imaging spectroscopy in the far-infrared with sub-arcsecond angular resolution. To provide further study of the technique and improve its technology readiness, we have constructed a laboratory-based DFI testbed. This instrument is coupled to a custom array of 25 feedback-controlled transition-edge sensor (TES) bolometers. We present the results of characterisation experiments to optimise the detector system as an integrated component of the DFI assembly. We demonstrate that tuning the proportional-integral-derivative (PID) feedback control loops of the detectors and the timing of the multiplexed measurement process can modify the detector array's noise performance and speed of response to optical modulation for this purpose. From these, we have determined a set of optimised detector settings that reduce spectral noise in the spatial-spectral interferometer by 37-79%. In addition, we present further thermal characterisation of the detector array.

A range-resolved laser interferometer is the leading candidate for providing displacement metrology that can meet the stringent precision and low power dissipation requirements of cryogenic space astronomy missions. In prior work, a three-phase homodyne laser interferometer was developed using a simple optical and signal processing scheme that achieved the desired dynamic performance required for state-of-the-art cryogenic far-infrared spectrometers, however, the system required three detectors and amplifiers, and exhibited poor performance at low speeds due to 1/f noise associated with the detector and electronics.(1, 2) A frequency modulation continuous wave (FMCW) heterodyne approach was subsequently adopted to address this shortcoming by shifting the signal of interest well away from the 1/f region.(1, 3) This technique provides the additional advantage of enabling simultaneous multiaxis measurements all using a single laser and a single detector. This paper discusses several applications of the multiaxis FMCW design that as currently implemented can provide simultaneous measurements of up to 8 axes. The need for a precise and intrinsically low power 1-D displacement metrology system to measure the optical path difference of a cryogenic Fourier transform spectrometer was the initial driver for this research; applications in N -dimensions are currently being explored. Several applications of the technique at both high and low speeds are considered, including multiaxis precision linear positioning, the simultaneous measurement of the cryogenic coefficients of thermal expansion for multiple materials, and cryogenic accelerometry. Results from these applications will be presented and used to discuss limitations of the technique.

The development status of a cryogenic far-infrared post-dispersed polarizing Fourier transform spectrometer is presented. Results will inform the design of such hybrid spectrometers proposed for future astronomical space observatories.

Optical fibers are commonly used for data transmission and sensing in industrial, geophysical, and aerospace markets, where they may be employed in high vacuum and cryogenic environments. The performance and integrity of optical fibers and their coatings is well understood over temperatures of ≈40 to 300 °C and pressures up to 100 atm, but their characteristics at cryogenic temperatures under high vacuum remain relatively unexplored. This study investigates the optical and mechanical reliability of selected fibers operating at cryogenic temperatures. The fiber samples under investigation were prepared with either an acrylate or polyimide coating. Several properties of the fibers were assessed, including optical loss, mechanical strength, and coating integrity. Optical loss was monitored continuously over a single temperature cycle from 300K to 4K and back. Additional samples were subjected to either one or three temperature cycles and held at 4K for extended periods. Mechanical strength of the thermally cycled fibers was determined via a 2-point bend method, and the coating material was characterized using Fourier transform infrared spectroscopy and thermogravimetric analysis.

Scientists must reconsider the design of cryogenically cooled spectrometers in order to fully exploit the ever-increasing sensitivity of superconducting far-infrared bolometers. While Fourier transform spectrometers (FTS) have an illustrious history in astronomical research, the sensitivity of modern detectors is such that the multiplex disadvantage of FTS is prohibitive unless the spectral bandpass can be restricted to a few tenths of one percent. One method of achieving this goal is to use a diffraction grating as a post-dispersing component. Unlike a typical FTS, in which a single detector simultaneously measures a broad spectral band, a post-dispersed detection system requires multiple detectors, each with their own unique spectral, spatial and temporal responses. Moreover, the narrow spectral band viewed by each detector results in an interferogram having a large coherence length. In general, the signal is heavily modulated, yet truncated. While simulations play a useful role in modeling instrumental performance, there is no substitute for data obtained from a real implementation of an instrument concept. In this paper we describe the development of a cryogenic, far-infrared, post-dispersed, polarizing FTS (PDPFTS). The end-to-end performance of the PDPFTS will be evaluated in a large cryogenic test facility to simulate a space environment. The results provide valuable insight into the spectral calibration and data processing challenges that will be faced by hybrid spectrometers employing a post-dispersed component.

The high spectral resolution mode of the SpicA FAR-infrared Instrument (SAFARI) is enabled by inserting a Fourier Transform Spectrometer (FTS), based on a Martin-Puplett interferometer, into the signal path of the instrument. The cryogenic FTS mechanism (FTSM) enables linear scans of two back-to-back rooftop mirrors sharing a common apex. ABB Inc. is under contract with the Canadian Space Agency to develop and test at 4 K an FTSM Engineering Demonstration Unit (EDU) for TRL-5 demonstration. The main SAFARI FTSM performance drivers are the stringent mechatronic demands (position stability of roof-top mirrors in step scan mode <10 nm RMS, velocity jitter in constant velocity mode <1% RMS at 85 µm/s, linear stroke <34 mm, error on position feedback laser metrology <10 nm RMS) and ultra-low photon leakage level from laser metrology (<1 pW), severely constrained by a tight thermal budget (heat dissipation <1.5 mW) under a specific micro-vibration environment (30 µg/√Hz external), all at cryogenic temperatures (4 K). In this paper, we describe the FTSM EDU developed and built at ABB with its laser metrology sensor. The FTSM EDU is based on a novel cryogenic design presented in 2020 using a reactionless and long-stroke flexure-based 4-bar linkage with stiffness compensation and a custom moving magnet actuator. Results from FTSM EDU room-temperature characterization and cryogenic proof-of-concept tests conducted at University of Lethbridge as a key step towards TRL-5 demonstration are discussed to assess the compliance of this novel design to the challenging cryogenic SAFARI FTSM performance requirements.

Future far-infrared space missions require highly-sensitive spectroscopy as a primary diagnostics tool. However, these systems are sensitive to straylight, due to the ultra-sensitive few-mode detectors used, which affects the measurement and calibration of the spectrum, as revealed by the Herschel mission. To ensure that the science goals of future missions are met, the complex modal behaviour has to be understood, and appropriate verification and calibration strategies must be developed. We propose a modal framework to addresses these issues, using Herschel-SPIRE as a case study, and demonstrate how the technique can be used for the design and verification of spectrometers in future far-infrared missions.

Scientists must reconsider the design of cryogenically cooled spectrometers in order to fully exploit the ever-increasing sensitivity of superconducting far-infrared bolometers. While Fourier transform spectrometers (FTS) have an illustrious history in astronomical research, the sensitivity of modern detectors is such that the multiplex disadvantage of FTS is prohibitive unless the spectral bandpass can be restricted to a few tenths of one percent. One method of achieving this goal is to use a diffraction grating as a post-dispersing component. Unlike a typical FTS, in which a single detector simultaneously measures a broad spectral band, a post-dispersed detection system requires multiple detectors, each with their own unique spectral, spatial and temporal responses. Moreover, the narrow spectral band viewed by each detector results in an interferogram having a large coherence length. In general, the signal is heavily modulated, yet truncated. While simulations play a useful role in modeling instrumental performance, there is no substitute for data obtained from a real implementation of an instrument concept. In this paper we describe the development of a cryogenic, far-infrared, post-dispersed, polarizing FTS (PDPFTS). The end-to-end performance of the PDPFTS will be evaluated in a large cryogenic test facility to simulate a space environment. The results provide valuable insight into the spectral calibration and data processing challenges that will be faced by hybrid spectrometers employing a post-dispersed component.

We have developed a modal framework [1], which uses the notion of optical modes, i.e. an unique set of individually coherent orthogonal field distributions, to propagate an incident electric field through an optical system. The framework relies on a transmission matrix and Singular Value Decomposition (SVD), to obtained the mode characteristics: their transmission efficiencies and spatial forms over the input and output surface of the optical system. Here, we present a VNA phase and amplitude measurement scheme used for determining the transmission matrix, and we compare the obtained mode characteristics to our model for a pair of limiting slits at 104 GHz, which show good agreement.

The continually increasing sensitivity required for the advancement of far-infrared astronomy dictates that the next generation of space-based observatories must employ cryogenically cooled telescopes and instrumentation. Operating cryogenic instrumentation in orbit poses several challenges, including the need for extremely low power dissipation and precise position measurement and control. In prior work, we reported on the development of a homodyne three-phase range-resolved laser interferometer, which demonstrated a displacement measurement uncertainty of 2:3nmrms at <4K.1 Effects of low frequency noise (1=f) in the electrical signals at low velocities were performance limiting due to the interpretation of noise as interference fringes. To avoid 1=f noise, a frequency-modulated continuous-wave (FMCW) heterodyne approach was adopted. An FMCW prototype was developed, and the preliminary results yielded an uncertainty of 29nmrms at <4K.2 In this paper we present the design of an integrated cryogenic FMCW range-resolved laser interferometer which features real time data processing for simultaneous displacement measurements of up to 8 axes. The performance of fibers and their coupling under ultra-high vacuum at cryogenic temperatures is largely unexplored, and we present the cryogenic characterization results of several key variables, including fiber type, termination, and mating, along with alignment effects due to the thermal contraction of fiber components. These results have been incorporated into the design of our cryogenic FMCW interferometer. Applications of cryogenic range resolved interferometry are discussed, with a focus on the integration of the FMCW interferometer with a custom 3-axis cryogenic accelerometer.

Modeling ultra-low-noise far-infrared grating spectrometers has become crucial for the next generation of far-infrared space observatories. Conventional techniques are awkward to apply because of the partially coherent form of the incident spectral field, and the few-mode response of the optics and detectors. We present a modal technique for modeling the behavior of spectrometers that allows for the propagation and detection of partially coherent fields, and the inclusion of straylight radiated by warm internal surfaces. We illustrate the technique by modeling the behavior of the long wavelength band of the proposed SAFARI instrument on the well-studied SPICA mission.

Recent advances in far-infrared detector technology have led to increases in raw sensitivity of more than an order of magnitude over previous state-of-the-art detectors. With such sensitivity, photon noise becomes the dominant noise component, even when using cryogenically cooled optics, unless a method of restricting the spectral bandpass is employed. The leading instrument concept features reflecting grating spectrometers to post-disperse the light that has been modulated by a polarizing Fourier transform spectrometer (FTS) onto a detector array, thereby reducing the photon noise on each detector. This paper describes the development of a cryogenic (4 K) reflection grating spectrometer which operates over the wavelength range from 285 µm–500 µm and was used to post-disperse the output from a room-temperature polarizing FTS. Measurements of the grating resolving power and diffraction efficiency are presented as a function of both wavelength and polarization to characterize the instrument performance

The sensitivity of state-of-the-art superconducting far-infrared (FIR) detectors is such that wideband spectroscopic observations will require techniques to reduce the spectral bandwidth of a detector to limit the photon noise from an astronomical source. The leading instrument concept features grating spectrometers to post-disperse the light that has been modulated by a polarising Fourier transform spectrometer (FTS) onto a detector array, thereby reducing the photon noise on each detector. While the principles of this method are understood, to date an integrated system has not been realized in the laboratory. We present the development of a fully cryogenic post-dispersed polarising FTS (PDPFTS). To assess the data processing challenges posed by this hybrid spectrometer realistic astronomical spectra are generated by combining line emission from a tunable THz photomixer source with continuum emission from a variable blackbody source.

Post-dispersed Fourier transform spectrometers are prime candidates for up- coming far-infrared space telescopes, which achieve background limited spectral sensitivity by few-mode detectors. Straylight effects in such hybrid systems are investigated using a partially coherent modelling technique.

Abstract We use the SPace Infrared telescope for Cosmology and Astrophysics (SPICA) project as a template to demonstrate how deep spectrophotometric surveys covering large cosmological volumes over extended fields (1– $15\, \rm{deg^2}$ ) with a mid-IR imaging spectrometer (17– $36\, \rm{\rm{\upmu m}}$ ) in conjunction with deep $70\, \rm{\rm{\upmu m}}$ photometry with a far-IR camera, at wavelengths which are not affected by dust extinction can answer the most crucial questions in current galaxy evolution studies. A SPICA-like mission will be able for the first time to provide an unobscured three-dimensional (3D, i.e. x, y, and redshift z) view of galaxy evolution back to an age of the universe of less than $\sim$ 2 Gyrs, in the mid-IR rest frame. This survey strategy will produce a full census of the Star Formation Rate (SFR) in the universe, using polycyclic aromatic hydrocarbons (PAH) bands and fine-structure ionic lines, reaching the characteristic knee of the galaxy luminosity function, where the bulk of the population is distributed, at any redshift up to $z \sim 3.5$ . Deep follow-up pointed spectroscopic observations with grating spectrometers onboard the satellite, across the full IR spectral range (17– $210\, \rm{\rm{\upmu m}}$ ), would simultaneously measure Black Hole Accretion Rate (BHAR), from high-ionisation fine-structure lines, and SFR, from PAH and low- to mid-ionisation lines in thousands of galaxies from solar to low metallicities, down to the knee of their luminosity functions. The analysis of the resulting atlas of IR spectra will reveal the physical processes at play in evolving galaxies across cosmic time, especially its heavily dust-embedded phase during the activity peak at the cosmic noon ( $z \sim 1$ –3), through IR emission lines and features that are insensitive to the dust obscuration.