## Fast and Accurate 3D PSF Computation for Fluorescence Microscopy

Jizhou Li, Feng Xue and Thierry Blu

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Outline

The point-spread function (PSF) of a microscope describes the response of this imaging system to a point source or object. A realistic and accurately calculated PSF model can significantly improve the performance of deconvolution microscopy and also the localization accuracy in single-molecule microscopy.

Among microscopy PSF models, Gibson-Lanni's (JOSA-A, **9**, 154–166, 1992) is particularly useful since it involves explicitly design and experimental physical parameters. It is based on Kirchhoff's diffraction integral formula:

where the phase term has an explicit expression involving several physical parameters, and denotes the Bessel function of the first kind of order zero. *k* is the wave number of the fluorescent light and NA the numerical aperture of the microscope.

Our approach is based on two ideas: first, express (approximate, actually) the function as a linear combination of rescaled Bessel functions,
where are complex-valued coefficients (to be determined by fitting), and are adequately chosen scaling factors; second, compute exactly Kirchhoff's integral by using the following antiderivative (*a* and *b* arbitrary):

Advantages of our algorithm:

- Two orders of magnitude faster than the quadrature approach (e.g., see PSF Generator) at same accuracy.
- Can be extended to other microscopy PSF models.

### Reference

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Matlab Software

The Matlab code available

here (220KB) is a demo that allows to generate and visualize 3D microscopy PSF based on the Gibson-Lanni model. To understand how to use these files, please read the file

README.txt to understand how to start the demo.

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Demo snapshot

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Conditions of use
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You are free to use this software for research purposes, but you should not
redistribute it without our consent. In addition, we expect you to include an
adequate citation and acknowledgment whenever you present or publish results that are based on it.