Since its invention centuries ago, the light microscope has become an essential tool in many scientific fields, and is the basic tool for imaging individual cells or structures in the life sciences. The basic motivation for using microscopes remains the same: to resolve features that cannot be seen by a naked eye, and consequently there is a constant strive to improve their resolution to and beyond the diffraction limit barrier. However, when imaging biological specimens, the resolution is usually compromised due to inhomogeneous optical characters of the specimen. This inhomogeneity causes distortions to the light emitted from the specimen, leading to degradation of the image quality. One of the options for improving the resolution is by deconvolution, using the linear dependency between the optical setup impulse response (PSF) and the object light reflectance in the linear imaging model. By evaluating the PSF, the image resolution can be improved by solving a direct or iterative inverse problem. Since the initial PSF strongly influences the final result, it is generally crucial to obtain a good estimate of the PSF. Another recent approach to improve the microscopic images is adaptive optics. Adapted from astronomy and high resolution retinal imaging, adaptive optics is based on measurement and correction of the emitted wave-front error by measuring it from a laser reference beam. However, when the reference beam also passes through phase deforming media or in the cases of rapidly changing- or significant phase errors, the resolution does not reach the diffraction limited value and a further improvement by PSF estimation approach could be advantageous. Taken together, distortion-resilient methods for PSF estimation could provide a powerful addition to the imaging toolbox.
Here, we present PEPSI (PSF estimation by projection of speckle pattern illumination), a new approach for estimating the transverse PSF when imaging through phase deforming media. The method is based on measuring the deformation of a speckle pattern illuminating a fluorescent object. The motivation for using a speckle pattern to measure the deformations arises from their random phase distribution: these random phases yield a pattern whose statistics are not affected by optical aberrations. Therefore, by illuminating the object with the speckle pattern, an objective measure of the phase errors of the imaging path can be obtained, irrespective of the illumination path`s phase aberrations. Since the speckle pattern is uniformly distributed throughout the field of view, PEPSI estimates the average PSF of the entire field of view from a single pattern projection, and is thus suitable for dealing with dynamic phase aberrations (not requiring prior calibrations or acquisition of multiple images(. Moreover, in cases where the aberrations are non-isoplanatic, the local PSF for selected areas in the field of view can be obtained by the same analysis on those areas. As a demonstration of the PSF estimation accuracy of PEPSI, we used the obtained PSF estimates to improve the resolution of microscopic images using a common iterative maximum likelihood-based image reconstruction algorithm. The easy integration of PEPSI to a commercial microscope, which only requires an additional diffuser in the microscope illumination path, is also demonstrated by improving a degraded image taken by a commercial epi-illuminated microscope.
