A Fast Spectrum-Recovery Method for Hadamard Transform Spectrometers Having Nonideal Masks

Abstract

A computationally inexpensive method is presented for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks. Normally, N measurements are required in order to recover an N-point spectrum; this method requires N + N0 measurements to be taken, where, typically, N0 ≤ 10. Once the additional measurements have been taken, only O( N[log2 N + 2]) arithmetic operations—mostly additions or subtractions—are needed in order to recover the spectrum; a conventional procedure requires O(2 N2) operations. Preliminary work for this method is minimal, requiring O( N) operations as opposed to O( N3) for a conventional procedure; this work needs to be done only once for a given spectrometer. The spectrum-estimate obtained is unbiased.

Highly Multiplexed Optically Sectioned Spectroscopic Imaging in a Programmable Array Microscope

“…2. If the mask is imperfect, the theory of distorted S-m atrices, which are designated S*, must be considered in order to recover c. 11,[26][27][28][29][30][31] Transverse Line Spread Functions in Second-Order Hadamard Systems. Numerical calculations of wide eld uorescence point spread functions (PSF) have been treated previously.…”

Virtual Column Method for Correcting Masking Effects in Hadamard Transform Systems

“…7,9,10 W hile the theory of mask effects has been treated quite extensively, a more limited literature exists documenting artifact-correcting procedures. [11][12][13][14] One problem of particular interest arises from a class of Hadamard systems that may exhibit echo artifacts even in the absence of errors in the mask itself. 9,10 The appearance of these artifacts depends on the length of the sequence, and information about the artifact-inducing phenomena can be inferred from the artifact behavior.…”

Hadamard Transform Microscope Fluorescence Image

“…In spectroscopic applications, Hadamard transform Raman, atomic emission, visible, and nearinfrared spectrometry have been demonstrated by Fateley's research group (1)(2)(3)(4). Other Hadamard transform spectroscopies have also been developed by other researchers in recent years (5)(6)(7)(8)(9).…”