Handbook of Real-Time Fast Fourier Transforms

1995 ◽  
Author(s):  
Winthrop W. Smith
Keyword(s):  
Real Time ◽  
Fourier Transforms ◽  
Fast Fourier Transforms

Real-time implementation of fast Fourier transforms

1988 ◽  
Author(s):  
HOSSEIN HAKIMMASHHADI ◽  
STEVEN GRINGERI
Keyword(s):  
Real Time ◽  
Fourier Transforms ◽  
Fast Fourier Transforms

scholarly journals Multiplexed Nanometric 3D Tracking of Microbeads using a FFT-Phasor Algorithm

2019 ◽  
Author(s):  
T. B. Brouwer ◽  
N. Hermans ◽  
J. van Noort
Keyword(s):  
Diffraction Pattern ◽  
Real Time ◽  
Single Molecule ◽  
Fourier Transforms ◽  
Magnetic Tweezers ◽  
Fast Fourier Transforms ◽  
Tracking Algorithm ◽  
Wide Field ◽  
3D Tracking ◽  
Chromatin Fibers

AbstractMany single-molecule biophysical techniques rely on nanometric tracking of microbeads to obtain quantitative information about the mechanical properties of biomolecules such as chromatin fibers. Their three-dimensional position can be resolved by holographic analysis of the diffraction pattern in wide-field imaging. Fitting this diffraction pattern to Lorentz Mie scattering theory yields the bead position with nanometer accuracy in three dimensions but is computationally expensive. Real-time multiplexed bead tracking therefore requires a more efficient tracking method. Here, we introduce 3D phasor tracking, a fast and robust bead tracking algorithm with nanometric localization accuracy in a z-range of over 10 µm. The algorithm is based on a 2D cross-correlation using Fast Fourier Transforms with computer-generated reference images, yielding a processing rate of up to 10.000 regions of interest per second. We implemented the technique in magnetic tweezers and tracked the 3D position of over 100 beads in real-time on a generic CPU. Its easy implementation, efficiency, and robustness can improve multiplexed biophysical bead tracking applications, especially where high throughput is required.SignificanceMicrobeads are often used in biophysical single-molecule manipulation experiments and accurately tracking their position in 3 dimensions is key for quantitative analysis. Holographic imaging of these beads allows for multiplexing bead tracking but image analysis can be a limiting factor. Here we present a 3D tracking algorithm based on Fast Fourier Transforms that is fast, has nanometric precision, is robust against common artifacts and is accurate over 10’s of micrometers. We show its real-time application for magnetic tweezers based force spectroscopy on more than 100 chromatin fibers in parallel, but we anticipate that many other bead-based biophysical essays can benefit from this simple and robust 3 phasor algorithm.

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