The phasor algorithm is a simple, model-free and non-iterative localization algorithm, described in [1]. It is based on the principle that the first Fourier coefficient of a Fourier transform of a 1D or 2D image will provide information about the major constituent in the image. In case of single molecule localization, the major constituent is the PSF of an emitter. The first Fourier coefficient will directly provide information about the position and the FWHM of the PSF in the horizontal and vertical directions. As phasor localization is a model-free localization algorithm, it performs much faster than traditional Gaussian-based methods, with equal localization accuracies in all dimensions.

 

Phasor localization perfoms best at relatively small ROI sizes compared to gaussian-based models. It is recommended to use a radius of 300nm (a total ROI size of 700x700nm). Astigmatic localization could benefit from slightly larger sub-image size if high signal-to-noise levels are achieved. The small ROI sizes are caused by the fact that the presence of high amounts of background in the ROI introduces errors in the phasor localization.

 

As phasor localization provides information about the width of the PSF in X and Y, it can be used for astigmatic 3D positioning. This requires a calibration curve (see Calibration of the imaging system). Be aware that the calibration curve is dependent on the size of the sub-image chosen for phasor! Use the same sub-image size for calibration and localization. As the ratio of the phasor magnitude is consistent amongst background levels, the calibration series can have a different background-to-noise ratio than the actual measurement.

 

The basic principle behind the technique consists of the following steps:

1. From the ROI around an approximate localization, perform a partial Fourier transformation and isolate the first Fourier coefficient in both X and Y direction.
2. Plot the real and imaginary parts of the 2 coefficients in a phasor diagram - a 2D plotting tool with real and imaginary axis.
3. Calculate the phase angles corresponding to the 2 coefficients. This is a direct value for the normalized position of the emitter in the ROI.
4. Calculate the phasor magnitudes. This is a value for the PSF width in X and Y.
5. Calculate the Z-position based on two defocus curves as described in [1,2], if applicable.