The design, analysis and application of a multiplexing hyperspectral imager is presented. The hyperspectral imager consists of a broadband digital light projector that uses a digital micromirror array as the optical engine to project light patterns onto a sample object. A single point spectrometer measures light that is reflected from the sample. Multiplexing patterns encode the spectral response from the sample, where each spectrum taken is the sum of a set of spectral responses from a number of pixels. Decoding in software recovers the spectral response of each pixel. A technique, which we call complement encoding, is introduced for the removal of background light effects. Complement encoding requires the use of multiplexing matrices with positive and negative entries. The theory of multiplexing using the Hadamard matrices is developed. Results from prior art are incorporated into a singular notational system under which the different Hadamard matrices are compared with each other and with acquisition of data without multiplexing (pointwise acquisition). The link between Hadamard matrices with strongly regular graphs is extended to incorporate all three types of Hadamard matrices. The effect of the number of measurements used in compressed sensing on measurement precision is derived by inference using results concerning the eigenvalues of large random matrices. The literature shows that more measurements increases accuracy of reconstruction. In contrast we find that more measurement reduces precision, so there is a tradeoff between precision and accuracy. The effect of error in the reference on the Wilcoxon statistic is derived. Reference error reduces the estimate of the Wilcoxon, however given an estimate of theWilcoxon and the proportion of error in the reference, we show thatWilcoxon without error can be estimated. Imaging of simple objects and signal to noise ratio (SNR) experiments are used to test the hyperspectral imager. The simple objects allow us to see that the imager produces sensible spectra. The experiments involve looking at the SNR itself and the SNR boost, that is ratio of the SNR from multiplexing to the SNR from pointwise acquisition. The SNR boost varies dramatically across the spectral domain from 3 to the theoretical maximum of 16. The range of boost values is due to the relative Poisson to additive noise variance changing over the spectral domain, an effect that is due to the light bulb output and detector sensitivity not being flat over the spectral domain. It is shown that the SNR boost is least where the SNR is high and is greatest where the SNR is least, so the boost is provided where it is needed most. The varying SNR boost is interpreted as a preferential boost, that is useful when the dominant noise source is indeterminate or varying. Compressed sensing precision is compared with the accuracy in reconstruction and with the precision in Hadamard multiplexing. A tradeoff is observed between accuracy and precision as the number of measurements increases. Generally Hadamard multiplexing is found to be superior to compressed sensing, but compressed sensing is considered suitable when shortened data acquisition time is important and poorer data quality is acceptable. To further show the use of the hyperspectral imager, volumetric mapping and analysis of beef m. longissimus dorsi are performed. Hyperspectral images are taken of successive slices down the length of the muscle. Classification of the spectra according to visible content as lean or nonlean is trialled, resulting in a Wilcoxon value greater than 0.95, indicating very strong classification power. Analysis of the variation in the spectra down the length of the muscles is performed using variography. The variation in spectra of a muscle is small but increases with distance, and there is a periodic effect possibly due to water seepage from where connective tissue is removed from the meat while cutting from the carcass. The spectra are compared to parameters concerning the rate and value of meat bloom (change of colour post slicing), pH and tenderometry reading (shear force). Mixed results for prediction of blooming parameters are obtained, pH shows strong correlation (R² = 0.797) with the spectral band 598-949 nm despite the narrow range of pH readings obtained. A likewise narrow range of tenderometry readings resulted in no useful correlation with the spectra. Overall the spatial multiplexed imaging with a DMA based light modulation is successful. The theoretical analysis of multiplexing gives a general description of the system performance, particularly for multiplexing with the Hadamard matrices. Experiments show that the Hadamard multiplexing technique improves the SNR of spectra taken over pointwise imaging. Aspects of the theoretical analysis are demonstrated. Hyperspectral images are acquired and analysed that demonstrate that the spectra acquired are sensible and useful.