Larson N M, Crosmun R, Talmi Y
Appl Opt. 1974 Nov 1;13(11):2662-8. doi: 10.1364/AO.13.002662.
We present a general mathematical framework within which the relative performance of singly multiplexed Hadamard transform spectrometers (HTS) and conventional scanning spectrometers (SS) may be compared. The theoretical multiplex advantage (Fellgett advantage) is calculated for spectrometers operating in two spectral regions. For the low energy region, i.e., infrared, the determined multiplex advantage F is (N/2)((1/2)) (N is tle number of slots), in accordance with predictions given by Fellgett. For the high spectral energy region, i.e., uv-vis, F = (x/2x )((1/2)), where x is the intensity of the spectal element sought and x is the average intensity produced across the whole spectrum. Our predictions are verified by computer simulation of various characteristic spectra. Based on these results, we arrive at some conclusions concerning the practical application of HTS systems.
我们提出了一个通用的数学框架，在此框架内可以比较单复用哈达玛变换光谱仪（HTS）和传统扫描光谱仪（SS）的相对性能。针对在两个光谱区域运行的光谱仪计算了理论复用优势（费尔盖特优势）。对于低能量区域，即红外区域，根据费尔盖特给出的预测，确定的复用优势F为（N/2）^（1/2）（N是狭缝数量）。对于高光谱能量区域，即紫外-可见区域，F = （x/2x）^（1/2），其中x是所寻求光谱元素的强度，x是整个光谱产生的平均强度。我们的预测通过对各种特征光谱的计算机模拟得到了验证。基于这些结果，我们得出了一些关于HTS系统实际应用的结论。
