| The optimization of a spectrochemical experiment is commonly based on reducing the relative amount of noise or increasing the signal-to-noise ratio (SNR). When the noise is due mainly to the detector and is statistically independent of the incident radiation, the multiplexing inherent in the Hadamard transform (HT) spectrometer can provide an improved spectrum-estimate. A spectrum-estimate can be further improved when any nonidealities in the system are compensated. In this dissertation, three spectrum-estimation methods for an HT spectrometer having a nonideal mask are discussed in terms of computational efficiency, statistical bias, and the mean-square error associated with a given estimate. The relative performances of the spectrum-recovery methods are presented with examples to help identify the sources of error for each method. In addition, the results obtained from computer simulations are used to verify the theoretical foundation of each method.;An efficient algorithm for the determination of permutations associated with fast Hadamard transform is also presented. The algorithm is reliable and computationally inexpensive.;The effect of a single defective mask element on the output SNR for an HT spectrometer having a stationary mask is also discussed. The single defective mask element can cause the decrease in output SNR from that of an HT spectrometer having a perfect mask and the decrease is dependent on the amount of energy incident on the defective element. The defective mask can be compensated by a method which both is computationally inexpensive and can be fully automated. |
