ℓ1-regularized maximum likelihood estimation with focused-spot illumination quadruples the diffraction-limited resolution in fluorescence microscopy.

Super-resolution fluorescence microscopy has proven to be a useful tool in biological studies. To achieve more than two-fold resolution improvement over the diffraction limit, existing methods require exploitation of the physical properties of the fluorophores. Recently, it has been demonstrated that achieving more than two-fold resolution improvement without such exploitation is possible using only a focused illumination spot and numerical post-processing. However, how the achievable resolution is affected by the processing step has not been thoroughly investigated. In this paper, we focus on the processing aspect of this emerging super-resolution microscopy technique. Based on a careful examination of the dominant noise source and the available prior information in the image, we find that if a processing scheme is appropriate for the dominant noise model in the image and can utilize the prior information in the form of sparsity, improved accuracy can be expected. Based on simulation results, we identify an improved processing scheme and apply it in a real-world experiment to super-resolve a known calibration sample. We show an improved super-resolution of 60nm, approximately four times beyond the conventional diffraction-limited resolution.

Analyzing the super-resolution characteristics of focused-spot illumination approaches.

SIGNIFICANCE: It is commonly assumed that using the objective lens to create a tightly focused light spot for illumination provides a twofold resolution improvement over the Rayleigh resolution limit and that resolution improvement is independent of object properties. Nevertheless, such an assumption has not been carefully examined. We examine this assumption by analyzing the performance of two super-resolution methods, known as image scanning microscopy (ISM) and illumination-enhanced sparsity (IES). AIM: We aim to identify the fundamental differences between the two methods, and to provide examples that help researchers determine which method to utilize for different imaging conditions. APPROACH: We input the same image datasets into the two methods and analyze their restorations. In numerical simulations, we design objects of distinct brightness and sparsity levels for imaging. We use biological imaging experiments to verify the simulation results. RESULTS: The resolution of IES often exceeds twice the Rayleigh resolution limit when imaging sparse objects. A decrease in object sparsity negatively affects the resolution improvement in both methods. CONCLUSIONS: The IES method is superior for imaging sparse objects with its main features being bright and small against a dark, large background. For objects that are largely bright with small dark features, the ISM method is favorable.

Achieving superresolution with illumination-enhanced sparsity.

Recent advances in superresolution fluorescence microscopy have been limited by a belief that surpassing two-fold resolution enhancement of the Rayleigh resolution limit requires stimulated emission or the fluorophore to undergo state transitions. Here we demonstrate a new superresolution method that requires only image acquisitions with a focused illumination spot and computational post-processing. The proposed method utilizes the focused illumination spot to effectively reduce the object size and enhance the object sparsity and consequently increases the resolution and accuracy through nonlinear image post-processing. This method clearly resolves 70nm resolution test objects emitting ~530nm light with a 1.4 numerical aperture (NA) objective, and, when imaging through a 0.5NA objective, exhibits high spatial frequencies comparable to a 1.4NA widefield image, both demonstrating a resolution enhancement above two-fold of the Rayleigh resolution limit. More importantly, we examine how the resolution increases with photon numbers, and show that the more-than-two-fold enhancement is achievable with realistic photon budgets.

Total variation regularized deconvolution for extended depth of field microscopy.

The depth of field of an optical system can be extended through a combination of point spread function (PSF) engineering and image processing. A phase mask inserted in the back aperture of the system creates a PSF that is focus-invariant over an extended depth. A digital deconvolution is then used to restore transverse resolution. The application and analysis of this technique to fluorescence microscopy is limited in the literature. In this paper we formalize a microscopy specific imaging model, and experimentally demonstrate a total variation regularized deconvolution approach. Results are compared to the Wiener filter.

Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems.

We have demonstrated a one-dimensional array of individually addressable electrowetting tunable liquid lenses that compensate for more than one wave of phase distortion across a wavefront. We report a scheme for piston control using tunable liquid lens arrays in volume-bound cavities that alter the optical path length without affecting the wavefront curvature. Liquid lens arrays with separately tunable focus or phase control hold promise for laser communication systems and adaptive optics.

Noise removal in extended depth of field microscope images through nonlinear signal processing.

Extended depth of field (EDF) microscopy, achieved through computational optics, allows for real-time 3D imaging of live cell dynamics. EDF is achieved through a combination of point spread function engineering and digital image processing. A linear Wiener filter has been conventionally used to deconvolve the image, but it suffers from high frequency noise amplification and processing artifacts. A nonlinear processing scheme is proposed which extends the depth of field while minimizing background noise. The nonlinear filter is generated via a training algorithm and an iterative optimizer. Biological microscope images processed with the nonlinear filter show a significant improvement in image quality and signal-to-noise ratio over the conventional linear filter.

Simulation of electrowetting lens and prism arrays for wavefront compensation.

A novel application of electrowetting devices has been simulated: wavefront correction using an array of electrowetting lenses and prisms. Five waves of distortion can be corrected with Strehl ratios of 0.9 or higher, utilizing piston, tip-tilt, and curvature corrections from arrays of 19 elements and fill factors as low as 40%. Effective control of piston can be achieved by placing the liquid lens array at the focus of two microlens arrays. Seven waves of piston delay can be generated with variation in focal length between 1.5 and 500 mm.

Quantitative phase microscopy through differential interference imaging.

An extension of Nomarski differential interference contrast microscopy enables isotropic linear phase imaging through the combination of phase shifting, two directions of shear, and Fourier space integration using a modified spiral phase transform. We apply this method to simulated and experimentally acquired images of partially absorptive test objects. A direct comparison of the computationally determined phase to the true object phase demonstrates the capabilities of the method. Simulation results predict and confirm results obtained from experimentally acquired images.

Quantitative structured-illumination phase microscopy.

We introduce a quantitative phase imaging method for homogeneous objects with a bright field transmission microscope by using an amplitude mask and a digital processing algorithm. A known amplitude pattern is imaged on the sample plane containing a thick phase object by placing an amplitude mask in the field diaphragm of the microscope. The phase object distorts the amplitude pattern according to its optical path length (OPL) profile, and the distorted pattern is recorded in a CCD detector. A digital processing algorithm then estimates the object's quantitative OPL profile based on a closed form analytical solution, which is derived using a ray optics model for objects with small OPL gradients.