Deconvolution by digital filtering from linear discriminate analysis
A quantitative optical microscopy arrangement is described. Specifically, a digital filter derived from linear discriminant analysis is described for recovering impulse responses in applications that may include photon counting from a high speed photodetector and applied to remove ringing distortions from impedance mismatch in multiphoton fluorescence microscopy. Training of the digital filter is achieved by defining temporally coincident and non-coincident transients and identifying the projection within filter-space that best separates the two classes. The training allows rapid data analysis by digital filtering. The LDA filter is also capable of recovering deconvolved impulses for single photon counting from highly distorted ringing waveforms from an impedance mismatched photomultiplier tube. The LDA filter is also successful in removing these ringing distortions from two-photon excited fluorescence micrographs and may extend the dynamic range of photon counting by about three orders of magnitude through minimization of detector paralysis.
1. A quantitative optical microscopy arrangement, comprising:
a light source configured to provide optical energy to a sample region;
a detector configured to receive light reflected from or emitted through the sample, the detector comprising:
an optical-voltaic converter configured to convert the received light into a representative voltage, wherein the optical-voltaic converter is configured to output the representative voltage as an impulse response; and
a digital deconvolution filter operatively connected to the optical-voltaic converter and configured to receive the representative voltage and deconvolve the impulse response, wherein the digital deconvolution filter includes a plurality of coefficients determined based on a linear discriminant analysis of the impulse response of the representative voltage.
2. The arrangement of claim 1 , further comprising:
a field programmable gate array coupled to the detector and configured to receive an output of the digital deconvolution filter and provide real-time counting of photons from the sample region.