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Phase-controlled homodyne 2(N+R)-port detection with R local oscillators is analyzed with the aim of reconstructing the quantum state of a correlated N-mode signal field. It is shown that both the (N+R)-fold joint count distributions and the N fold j-oint difFerence-count distributions contain all knowable information on the state of the field. ln any case, the minimum number of local oscillators is given by the number of difFerent signal-field frequencies. Two Fourier integrals per mode are found to be required to reconstruct the density matrix of the signal field from the joint difFerence-count distributions measured in balanced homodyning. To illustrate the theory, it is applied to balanced homodyne 4N-port detection (R =N). In this scheme, the joint difFerence-count distributions directly yield the joint field-strength distributions of a correlated N-mode signal field. PACS number(s): 42.50.Dv, 42.50.Ar, 03.65.Bz

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Thermo-mechanical fatigue (TMF) data are needed for dimensioning of safety-critical parts, e.g. in power generation and in transportation by air, rail and road, and for designing of components, which operate at higher levels of efficiency and safety for longer periods of time. However, the current lack of a validated international standard for TMF leads to non-reproducibility of TMF data with negative implications on the design and economy of operation of many components. While a preliminary draft TMF standard has been written under the auspices of the International Standards Organisation (ISO), the "TMF-STANDARD" project addresses this issue at the European level, within the GROWTH programme of Framework Programme 5 funded by the European Commission.The R&D work in the TMF-Standard project has been started with the preparation of an inventory of institutions in the EU and the pre-accession states that perform TMF testing, and the testing methods and procedures which they apply. Afterwards, extensive pre-normative testing work has been carried out, the results of which have been considered in the drafting of a preliminary Codeof-Practice (CoP) that forms the base for the current validation round robin testing. The results of the validation tests are going to be subjected to statistical analysis, in order to substantiate the formulation of a validated CoP on strain-controlled TMF testing. The present paper summarizes the main objectives and achievements obtained so far within the TMF-Standard project, and gives an outlook on the further activities of the project.