Because optical systems have huge bandwidth and are capable of generating low noise short pulses they are ideal for undersampling multi-band signals that are located within a very broad frequency range. In this paper we propose a new scheme for reconstructing multi-band signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The scheme, which we call multi-rate sampling (MRS), entails gathering samples at several different rates whose sum is significantly lower than the Nyquist sampling rate. The number of channels does not depend on any characteristics of a signal. In order to be implemented with simplified hardware, the reconstruction method does not rely on the synchronization between different sampling channels. Also, because the method does not solve a system of linear equations, it avoids one source of lack of robustness of previously published undersampling schemes. Our simulations indicate that our MRS scheme is robust both to different signal types and to relatively high noise levels. The scheme can be implemented easily with optical sampling systems. I. INTRODUCTIONA multi-band signal is one whose energy in the frequency domain is contained in the finite union of closed intervals. A sparse signal is a signal that occupies only a small portion of a given frequency region. In many applications of radars and communications systems it is desirable to reconstruct a multi-band sparse signal from its samples. When the signal bands are centered at frequencies that are high compared to their widths, it is not cost effective and often it is not feasible to sample at the Nyquist rate F nyq ; the rate that for a real signal is equal to twice the maximum frequency of the given region in which the signal spectrum is located. It is therefore desirable to reconstruct the signal by undersampling; that is to say, from samples taken at rates significantly lower than the Nyquist rate. Sampling at any constant rate that is lower than the Nyquist rate results in down-conversion of all signal bands to a low frequency region called a baseband. This creates two problems in the reconstruction of the signal. The first is a loss of knowledge of the actual signal frequencies. The second is the possibility of aliasing; i.e. spectrum at different frequencies being down-converted to the same frequency in the baseband.Optical systems are capable of very high performance undersampling [1]. They can handle signals whose carrier frequency can be very high, on the order of 40 GHz, and signals with a dynamic range as high as 70 dB. The size, the weight, and the power consumption of optical systems make them ideal for undersampling. The simultaneous sampling of a signal at different time offsets or at different rates can be performed efficiently by using techniques based on wavelength-division multiplexing (WDM) that are used in optical communication systems.There is a vast literature on reconstructing signals from undersampled data. Landau proved that, regardles...

Frequency domain multiplexing (FDM) is the baseline readout system for the Xray Integral Field Unit (X-IFU) on board the Athena mission. Under the FDM scheme, TESs are coupled to a passive LC filter and biased with alternating current (AC bias) at MHz frequencies. Using high-quality factor LC filters and room temperature electronics developed at SRON and low-noise two-stage SQUID amplifiers provided by VTT, we have recently demonstrated good performance with the FDM readout of Mo/Au TES calorimeters with Au/Bi absorbers. We have achieved a performance requested for the demonstration model (DM) with the single pixel AC bias (∆ E =1.8 eV) and 9 pixel multiplexing (∆ E =2.6 eV) modes. We have also demonstrated 14-pixel multiplexing with an average energy resolution of 3.3 eV, which is limited by non-fundamental issues related to FDM readout in our lab setup.

We are developing the frequency domain multiplexing (FDM) read-out of transition-edge sensor (TES) microcalorimeters for the X-ray Integral Field Unit (X-IFU) instrument on board of the future European X-Ray observatory Athena. The X-IFU instrument consists of an array of ∼3840 TESs with a high quantum efficiency (>90 %) and spectral resolution ∆E=2.5 eV @ 7 keV (E/∆E ∼2800). FDM is currently the baseline readout system for the X-IFU instrument. Using high quality factor LC filters and room temperature electronics developed at SRON and low-noise two stage SQUID amplifiers provided by VTT, we have recently demonstrated good performance with the FDM readout of Mo/Au TES calorimeters with Au/Bi absorbers. An integrated noise equivalent power resolution of about 2.0 eV at 1.7 MHz has been demonstrated with a pixel from a new TES array from NASA/Goddard (GSFC-A2). We have achieved X-ray energy resolutions ∼2.5 eV at AC bias frequency at 1.7 MHz in the single pixel read-out. We have also demonstrated for the first time an X-ray energy resolution around 3.0 eV in a 6 pixel FDM read-out with TES array (GSFC-A1). In this paper we report on the single pixel performance of these microcalorimeters under MHz AC bias, and further results of the performance of these pixels under FDM.

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