Accuracy of spectrum estimate in fluorescence spectral microscopy with spectral filters

We establish the accuracy of the spectrum that is estimated with an inexpensive fluorescence spectral microscope utilizing a small set of spectral filters [Soriano et al, Opt. Exp. 10, 1458–1464 (2002)]. The spectrum at an arbitrary image location of the fluorescent sample is estimated as a linear superposition of basis spectra that are derived by singular value decomposition (SVD) or principal component analysis (PCA) from a spectral library of fluorescence spectra. Estimation performance is analyzed as a function of library statistics, filter selection and sequencing, minimum negativity constraint and signal to noise ratio (SNR) of fluorescence image. We consider image SNR degradations that arise from weakening of image intensity, additive Gaussian noise, intensity-dependent Poisson noise and quantization errors. The recovery of specific spectral features like spectral resolution, general similarity and peak alignments, is assessed using Linfoot’s criteria of fidelity, structural content, and correlation. We found that estimation with SVD basis spectra is more robust against image noise than that with PCA basis spectra. However for high SNR images, accurate estimation is achieved more quickly with PCA basis spectra and with better response to the application of minimum negativity constraint.