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An optical Fourier transform coprocessor with direct phase determination.

ABSTRACT: The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symmetries of the Fourier transform we are able to determine the phase directly from straightforward intensity measurements, creating an optical Fourier transform with O(n) apparent complexity. Performing larger optical Fourier transforms requires higher resolution spatial light modulators, but the execution time remains unchanged. This method could unlock the potential of the optical Fourier transform to permit 2D complex-to-complex discrete Fourier transforms with a performance that is currently untenable, with applications across information processing and computational physics.

SUBMITTER: Macfaden AJ

PROVIDER: S-EPMC5651838 | biostudies-literature | 2017 Oct

REPOSITORIES: biostudies-literature

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An optical Fourier transform coprocessor with direct phase determination.

Macfaden Alexander J AJ Gordon George S D GSD Wilkinson Timothy D TD

Scientific reports 20171020 1

The Fourier transform is a ubiquitous mathematical operation which arises naturally in optics. We propose and demonstrate a practical method to optically evaluate a complex-to-complex discrete Fourier transform. By implementing the Fourier transform optically we can overcome the limiting O(nlogn) complexity of fast Fourier transform algorithms. Efficiently extracting the phase from the well-known optical Fourier transform is challenging. By appropriately decomposing the input and exploiting symm ...[more]

PMID: 29057903

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Project description:Fourier transform infrared (FTIR) spectroscopy, a technology traditionally used in chemistry to determine the molecular composition of a wide range of sample types, has gained growing interest in microbial typing. It is based on the different vibrational modes of the covalent bonds between atoms of a given sample, as bacterial cells, induced by the absorption of infrared radiation. This technique has been largely used for the study of pathogenic species, especially in the clinical field, and has been proposed also for the typing at different subspecies levels. The high throughput, speed, low cost, and simplicity make FTIR spectroscopy an attractive technique also for industrial applications, in particular, for probiotics. The aim of this study was to compare FTIR spectroscopy with established genotyping methods, pulsed-field gel electrophoresis (PFGE), whole-genome sequencing (WGS), and multilocus sequence typing (MLST), in order to highlight the FTIR spectroscopy potential discriminatory power at strain level. Our study focused on bifidobacteria, an important group of intestinal commensals generally recognized as probiotics. For their properties in promoting and maintaining health, bifidobacteria are largely marketed by the pharmaceutical, food, and dairy industries. Strains belonging to Bifidobacterium longum subsp. longum and Bifidobacterium animalis subsp. lactis were taken into consideration together with some additional type strains. For B. longum subsp. longum, it was possible to discriminate the strains with all the methods used. Although two isolates were shown to be strictly phylogenetically related, constituting a unique cluster, based on PFGE, WGS, and MLST, no clustering was observed with FTIR. For B. animalis subsp. lactis group, PFGE, WGS, and MLST were non-discriminatory, and only one strain was easily distinguished. On the other hand, FTIR discriminated all the isolates one by one, and no clustering was observed. According to these results, FTIR analysis is not only equivalent to PFGE, WGS, and MLST, but also for some strains, in particular, for B. animalis subsp. lactis group, more informative, being able to differentiate strains not discernible with the other two methods based on phenotypic variations likely deriving from certain genetic changes. Fourier transform infrared spectroscopy has highlighted the possibility of using the cell surface as a kind of barcode making tracing strains possible, representing an important aspect in probiotic applications. Furthermore, this work constitutes the first investigation on bifidobacterial strain typing using FTIR spectroscopy.

Dataset Information

An optical Fourier transform coprocessor with direct phase determination.

Publications

An optical Fourier transform coprocessor with direct phase determination.

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