Bandpass correction in spectrometer measurements using monochromators is often necessary in order to obtain accurate measurement results. The classical approach of spectrometer bandpass correction is based on local polynomial approximations and the use of finite differences. Here we compare this approach with an extension of the Richardson-Lucy method, which is well known in image processing, but has not been applied to spectrum bandpass correction yet. Using an extensive simulation study and a practical example, we demonstrate the potential of the Richardson-Lucy method. In contrast to the classical approach, it is robust with respect to wavelength step size and measurement noise. In almost all cases the Richardson-Lucy method turns out to be superior to the classical approach both in terms of spectrum estimate and its associated uncertainties.

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Introduction Weight, proportion and distribution of fat and muscle in beef carcasses are of importance in order to maximise economic value and reduce waste. In-vivo ultrasound-measured predictors of cattle carcass composition could be of use when taken at the beginning of the finishing period (to allocate feeding groups and levels or for early selection of potential breeding stock), or pre-slaughter (to market-select finished animals, sort carcasses on quality, or feed back information from slaughter animals to breeding programmes). The aims of this study were to investigate the ability of ultrasound-measured fat and muscle depths to predict carcass composition and tissue distribution and to quantify the relative accuracy of predictions using ultrasound measurement taken at the start or end of the finishing period. Materials and methodsLive weight (LWT) and ultrasound measurements (muscle depth (UMD) and four fat depths (UFD) over the 3 rd lumbar vertebra; four UFD measurements over the 12 th thoracic vertebra) were measured on 52 crossbred steers and 10 heifers at the start and end of the finishing period (average age 482 and 576 d, respectively). Animals were slaughtered in batches, depending on weight and visual predictions of carcass grade, and one carcass side was fully dissected. Stepwise multiple linear regression analyses were performed in Genstat (Payne et al., 2005) to determine the best combinations of predictor traits (LWT, UMD, UFD) to predict: total weights of fat and muscle in the carcass side (CF and CM, respectively), the forequarter (FQF, FQM) and hindquarter (HQF, HQM); CF and CM as proportions of carcass side weight (CF%SD, CM%SD); FQF and FQM as proportions of carcass side weight (FQF%SD, FQM%SD); HQF and HQM as proportions of carcass side weight (HQF%SD, HQM%SD); HQF as a proportion of total fat weight in the carcass side (HQF%F); HQM as a proportion of total muscle weight in the carcass side (HQM%M). Three models (M1-M3) were tested for each carcass trait that used LWT and informative ultrasound data from: (1) prefinishing; (2) post-finishing; or (3) pre-finishing and post-finishing. Individual UFD measurements (max. 8, if all contributed towards a reduction in residual standard deviation) were used in the models, rather than averaging UFD measurements at each site. Only LWT and UMD were tested in models to predict muscle traits and only LWT and UFD were used in models to predict fat traits, in order to minimise confounding between fat and muscle traits. ResultsAs expected, higher prediction accuracies (adjusted R 2 ) were generally achieved using measurements taken postfinishing than pre-finishing, although combining both substantially increased adjusted R 2 values (Table 1). Fat weights and proportions (of total carcass side) were predicted with higher accuracy than muscle traits. For muscle traits, weights were predicted more accurately than their proportions, whereas there was an opposite trend for fat traits. The proportion of the carcass side weight consisting of muscle in the forequ...