Can phase masks extend depth-of-field in localization microscopy?

Abstract

In localization microscopy, the position of isolated fluorescent emitters are estimated with a resolution better than the diffraction limit. In order to image thick samples, which are common in biological applications, there is considerable interest in extending the depth-of-field of such microscopes in order to make their accuracy as invariant as possible to defocus. For that purpose, we propose to optimize annular binary phase masks placed in the pupil of the microscope in order to generate a point spread function for which the localization accuracy is almost invariant along the optical axis. The optimization criterion is defined as the localization accuracy in the plane expressed in terms of the Cramér-Rao bound. We show that the optimal masks significantly increase the depth-of-field of single-molecule imaging techniques relatively to an usual microscope objective.

Influence of high numerical aperture on depth-of-field enhancing phase mask optimization in localization microscopy

“…Note that although the results presented in this article are limited to phase masks with circular symmetry, they can easily be extended to the many types of phase masks proposed in the literature to improve the DoF [13][14][15][16][17][18]. As already mentioned, annular binary phase masks are easy to manufacture and they have been shown to extend DoF in localization microscopy [4,5]. This type of mask is based on concentric rings implementing static spatial phase modulations of alternatively 0 and π radians at a nominal wavelength λ as illustrated in Fig.…”

“…According to Ref. [4], the RCRB also depends on the sub-pixel position of the PSF relatively to the pixel grid (i.e., the "phasing"). The largest value of the RCRB (which corresponds to the worst localization precision) is obtained when the PSF is centered on a pixel of the sensor.…”

“…The largest value of the RCRB (which corresponds to the worst localization precision) is obtained when the PSF is centered on a pixel of the sensor. In this case, and in the presence of emitter shot noise only, the RCRB along the x and y-axis directions has the same value and can be calculated as follows [4]:…”

“…Among them, we have proposed a method based on annular binary phase masks, which are easy to manufacture. After proper optimization and appropriate signal processing, they have been shown to be able to improve the DoF by a factor 3 [4,5].…”

How to assess depth-of-field extension strategies applied to single-molecule super-resolution microscopes?

“…It shows that this new detection criterion gives rise to phase masks with better probability of detection while preserving localization precision. This methodology also allows us to perform a quantitative comparison, in terms of both localization precision and detection capacity, between the phase masks previously developed in the literature [2,3,7] and the binary annular phase masks recently proposed by our team [8].…”