Optical design in the terahertz (THz) waveband can be challenging, especially for high-precision applications. In this
paper we summarise our experience with the quasi-optical design and subsequent performance of astronomical
telescopes designed to measure the faint temperature and polarisation properties of the Cosmic Microwave Background
Radiation, in particular QUaD<sup>1</sup>, the PLANCK Surveyor<sup>2</sup> and MBI<sup>3</sup>. These telescopes contain a range of quasi-optical
components including corrugated feed horns, on- and off-axis conic mirrors and lenses. Knowledge of their optical
performance and beam patterns is critical for understanding systematic effects in the reliable extraction of feeble
Although Physical Optics can be used to characterise electromagnetic systems to high accuracy, it is computationally
intensive at these frequencies and often not suitable for the initial design or preliminary analysis of large multi-element
optical systems. In general there is a lack of dedicated software tools for modelling the range of components and
propagation conditions encountered in typical systems and we have employed a variety of commercial and in-house
software packages for this task. We describe the techniques used, their predictions and the performance of the
telescopes that have been measured to-date.
MODAL is an optical design and analysis package targeting the millimetre and sub-millimetre region of the
electromagnetic spectrum. It is being developed at NUI Maynooth with the aim of integrating advanced modelling
techniques and access to High Performance Computing into a user-friendly and yet very powerful tool for an
(quasi-)optical designer. MODAL has been recently extended to allow integrated simulation of custom corrugated
horns and dielectric lenses. This made it possible to model an existing instrument (QUaD), with the goal of
optimising its performance.
Here we present new results from analysis of the predicted performance of the QUaD telescope, with particular
emphasis on polarisation information. They were obtained by using MODAL to model the whole telescope, with
the distortion of the primary accounted for, for a range of component tilts and separations.
In the presentation we report on novel applications of Gaussian beam mode (GBM) analysis, including in image
deconvolution and Fourier grating design.
GBMs are the natural modes with which to describe propagation of quasi-collimated long-wavelength beams, with only
a small number of modes required to reach adequate accuracy for many practical applications. GBMs provide a more
efficient and natural basis set with which to describe propagation than for example plane wave decomposition,
especially because of the limited spatial frequency content (only a few degrees of freedom are necessary to describe
such beams and the degrees of freedom can be associated with component GBMs).
We discuss how GBM analysis provides a useful alternative scheme to FFT approaches for performing deconvolutions
and image retrieval in long-wavelength quasi-collimated systems. The convolving beam is usually described very
efficiently in terms of beam modes and an SVD approach can be used to extract the mode coefficients of the
deconvolved image. We discuss in particular the novel application to mapping in astronomical telescope observations.
Another useful area of application is in the design of Fourier phase gratings. Fourier gratings can be used for beam
multiplexing of local oscillator power in array imaging systems. In this case phase retrieval is often driven by an
iterative approach to the solution based on FFTs and thus by implication plane waves. A GBM approach leads to a more
efficient and physically more meaningful approach, especially again because of the limited spatial frequencies possible
in long wavelength systems.
QUaD is a ground-based high-resolution (up to l ≈ 2500) instrument designed to map the polarisation of the Cosmic Microwave Background and to measure its E-mode and B-mode polarisation power spectra. QUaD comprises a bolometric array receiver (100 and 150 GHz) and re-imaging optics on a 2.6-m Cassegrain telescope 2. It will operate for two years and begin observations in 2005. CMB polarisation measurements will require not only a significant increase in sensitivity over earlier experiments but also a better understanding and control of systematic effects particularly those that contribute to the polarised signal. To this end we have undertaken a comprehensive quasi-optical analysis of the QUaD telescope. In particular we have modelled the effects of diffraction on beam propagation through the system. The corrugated feeds that couple radiation from the telescope to phase-sensitive bolometers need to have good beam symmetry and low sidelobe levels over the required bandwidth. It is especially important that the feed horns preserve the polarisation orientation of the incoming fields. We have used an accurate mode-matching model to design such feed horns. In this paper we present the diffraction analysis of the QUaD front-end optics as well as the electromagnetic design and testing of the QUaD corrugated feeds.
Optical design in the terahertz (THz) waveband suffers from a lack of dedicated software tools for modelling the range of electromagnetic and quasi-optical propagation conditions encountered in typical systems. Optical engineers are forced to use packages written for very different wavelength systems and there is often a lack of confidence in the results because of possible inappropriate underlying physical models. In this paper we describe the analytical techniques and dedicated CAD software tools (MODAL) that we are developing for long-wavelength design and analysis in the THz waveband. Our basic approach to modelling long-wavelength propagation is the application of modal analysis appropriate to the problem under investigation. We have extended this to include the efficient description of common off-axis (tilted) components such as simple curved reflectors. In earlier research we have investigated the conditions under which approximate methods (ray tracing, paraxial modes) can provide extremely efficient and accurate solutions and situations where a more rigorous approach is required. As a rigorous model of electromagnetic wave propagation, physical optics can be used to characterize complete systems to high accuracy. However, the straightforward approach is computationally intensive and, therefore, not suitable for the initial design or preliminary analysis of large multi-element optical systems. In order to improve the computational efficiency of the usual PO approach we have developed fast physical optics software, initially for the analysis of the ESA PLANCK system. The MODAL code is modular and multi-platform, and different propagation models can be used within the same framework. Distributed parallel computing enables significant reduction of the time needed to perform the calculations. We present the new software and analyses of the QuaD and Herschel (HIFI) telescope systems.
We look at anticipated science results achievable with QUaD, a ground-based experiment to measure the polarization of the CMB from the South Pole, and describe the features that will enable it to measure this weak polarized signal. We show that QUaD can make a high resolution measurement of the polarization signals on small angular scales. This will lead to tighter constraints on the key cosmological parameters and could also put new limits on the inflationary model.
HIFI is one of the three instruments for the Herschel Space Observatory, an ESA cornerstone mission. HIFI is a high resolution spectrometer operating at wavelengths between 157 and 625 μm. The need for a compact layout reducing the volume and mass as much as possible has important consequences for the optical design. Many mirrors are located in the near-field of the propagating beam. Especially in the long wavelength limit diffraction effects might therefore introduce significant amplitude and phase distortions. A classical geometrical optical approach is consequently inadequate. In this paper we present a rigorous quasi-optical analysis of the entire
optical system including the signal path, local oscillator path and onboard calibration source optical layout. In order to verify the results of the front-to-end coherent propagation of the detector beams, near-field measurement facilities capable of measuring both amplitude and phase have beam developed. A remarkable feature of these facilities is that the absolute coordinates of the measured field components are known to within fractions of a wavelength. Both measured and simulated fields can therefore compared directly since they are referenced to one single absolute position. We present a comparison of experimental data with software predictions obtained from the following packages: GRASP (Physical Optics Analysis) and GLAD (Plane Wave Decomposition).
We also present preliminary results for a method to correct for phase aberrations and optimize the mirror surfaces without changing the predesigned mechanical layout of the optical system.