Frequency shift algorithm: Application to a frequency-domain multiplexing readout of x-ray transition-edge sensor microcalorimeters.

In the frequency-domain multiplexing (FDM) scheme, transition-edge sensors (TESs) are individually coupled to superconducting LC filters and AC biased at MHz frequencies through a common readout line. To make efficient use of the available readout bandwidth and to minimize the effect of non-linearities, the LC resonators are usually designed to be on a regular grid. The lithographic processes, however, pose a limit on the accuracy of the effective filter resonance frequencies. Off-resonance bias carriers could be used to suppress the impact of intermodulation distortions, which, nonetheless, would significantly affect the effective bias circuit and the detector spectral performance. In this paper, we present a frequency shift algorithm (FSA) to allow off-resonance readout of TESs, while preserving the on-resonance bias circuit and spectral performance, demonstrating its application to the FDM readout of an x-ray TES microcalorimeter array. We discuss the benefits in terms of mitigation of the impact of intermodulation distortions at the cost of increased bias voltage and the scalability of the algorithm to multi-pixel FDM readout. We show that with FSA, in the multi-pixel and frequencies shifted on-grid, the line noises due to intermodulation distortion are placed away from the sensitive region in the TES response and the x-ray performance is consistent with the single-pixel, on-resonance level.

Three-dimensional dose distribution for partial irradiation of rat parotid glands with 200kV X-rays.

PURPOSE: To investigate dose distributions in partial-volume irradiation experiments in small experimental animals, in particular the parotid gland of rat. MATERIALS AND METHODS: High-resolution magnetic resonance imaging images were made that provided the outlines of the parotid glands, which were used to design collimators with conformal radiation ports for 100 and 50% cranial/caudal partial-volume irradiation. A protocol for absolute dosimetry was designed and relative dose measurements were performed. From the three-dimensional topographical data and the three-dimensional dose distribution, dose-volume histograms were determined. RESULTS: The standard uncertainty of absorbed entrance dose was within 3%. Radiochromic film, thermoluminescence dosemeters and ionization chamber dose measurements revealed that the relative doses measured were in good agreement. The 20-80% penumbra of the beam across the 50% field edge was only 0.4 mm at a 6 mm depth. The gradient of the percentage depth dose from the skin of the rat to a depth of 12 mm was 1.5% mm(-1). The absorbed doses in the cranial 50% and the caudal 50% partial volumes were comparable. This finding was reflected in the calculated dose-volume histograms of the different regions, which were similar. The dose in the shielded area between the left and right ports was about 14% of the dose near the centres of the beams. CONCLUSION: The designed set-up showed that irradiation of small volumes could be performed with high accuracy allowing the study of differences in radiation damage. Similar doses were given to the 50% cranial and 50% caudal gland volumes and, therefore, a possible difference in radiosensitivity in these volumes was not a dose effect. The approach used was also applicable for the irradiation of small volumes of other tissues.

Detector line spread functions determined analytically by transport of Compton recoil electrons.

To achieve the maximum benefit of conformal radiation therapy it is necessary to obtain accurate knowledge of radiation beam penumbras based on high-resolution relative dosimetry of beam profiles. For this purpose there is a need to perform high-resolution dosimetry with well-established routine dosimeters, such as ionization chambers or diodes. Profiles measured with these detectors must be corrected for the dosimeter's nonideal response, caused by finite dimensions and, in the case of an ionization chamber, the alteration of electron transport and a contribution of electrons recoiled in the chamber wall and the central electrode. For this purpose the line spread function (LSF) of the detector is needed. The experimental determination of LSFs is cumbersome and restricted to the specific detector and beam energy spectrum used. Therefore, a previously reported analytical model [Med. Phys. 27, 923-934 (2000)] has been extended to determine response profiles of routine dosimeters: shielded diodes and, in particular, ionization chambers, in primary dose slit beams. The model combines Compton scattering of incident photons, the transport of recoiled electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. It yields the traveling direction and the energy of electrons upon incidence on the detector surface. In the case of ionization chambers, geometrical considerations are then sufficient to calculate the relative amount of ionization in chamber air, i.e., the detector response, as a function of the detector location in the slit beam. In combination with the previously reported slit beam dose profiles, the LSF can then readily be derived by reconstruction techniques. Since the spectral contributions are preserved, the LSF of a dosimeter is defined for any beam for which the effective spectrum is known. The detector response profiles calculated in this study have been verified in a telescopic slit beam geometry, and were found to correspond to experimental profiles within 0.2 and 0.3 mm (full width at half-maximum) for a Wellhoefer IC15 chamber in a 6 and 25 MV-X x-ray beam, respectively. For a shielded diode these figures were found to be 0.2 and 0.1 mm, respectively. It is shown that a shielded diode in a primary beam needs only a small size-based correction of measured profiles. The effect of the LSF of an IC15 chamber on penumbra width has been determined for a set of model penumbras. The LSFs calculated by the application of the analytical model yield a broadening by 2 mm of a 3 mm wide penumbra (20%-80%). This is 0.5 mm (6 MV-X) to 1 mm (25 MV-X) smaller than found with the experimental LSFs. With a spatial correction based on the LSFs that were determined in this study, this broadening of up to 2 mm is eliminated, so that ionization chambers like the IC15 can be used for high-resolution relative dosimetry on a routine basis.

Slit x-ray beam primary dose profiles determined by analytical transport of Compton recoil electrons.

Accurate measurement of radiation beam penumbras is essential for conformal radiotherapy. For this purpose a detailed knowledge of the dosimeter's spatial response is required. However, experimental determination of detector spatial response is cumbersome and restricted to the specific detector type and beam spectrum used. A model has therefore been developed to calculate in slit beam geometry both dose profiles and detector response profiles. Summations over representative photon beam spectra yield profiles for polyenergetic beams. In the present study the model is described and resulting dose profiles verified. The model combines Compton scattering of incident photons, transport of resulting electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. This analytic model thus yields line spread kernels of primary dose in a water phantom. It is shown that the spatial response of an ideal point detector to a primary photon beam can be well described by the model; the calculations are verified by measurements with a diamond detector in a telescopic slit geometry in which all dose contributions except for the primary dose can be excluded. Effects of photon detector behavior, source size of the linear accelerator (linac) and detector size are studied. Measurements show that slit dose profiles calculated by means of the kernel are accurate within 0.1 mm of the full-width at half-maximum. For a theoretical point source and point detector combined with a 0.2 mm wide slit, the full-width half-maximum values of the slit beam dose profiles are calculated as 0.37 mm and 0.42 mm in a 6 MV and 25 MV x-ray beam, respectively. The present study shows that the model is adequate to calculate local dose effects that are dominated by approximately mono-directional, primary photon fluence. The analytic model further provides directional electron fluence information and is designed to be applied to various detectors and linac beam spectra.