Confocal scanning microscopy, a form of optical sectioning microscopy, has radically transformed optical imaging in biology. These devices provide a powerful means to eliminate from images the background caused by out-of-focus light and scatter. Confocal techniques can also improve the resolution of a light microscope image beyond what is achievable with widefield fluorescence microscopy. The quality of the images obtained, however, depends on the user's familiarity with the optical and fluorescence concepts that underlie this approach. We describe the core concepts of confocal microscopes and important variables that adversely affect confocal images. We also discuss data-processing methods for confocal microscopy and computational optical sectioning techniques that can perform optical sectioning without a confocal microscope.

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Optical sectioning microscopy.

Nowadays, magnetic hyperthermia constitutes a complementary approach to cancer treatment. The use of magnetic particles as heating mediators, proposed in the 1950s, provides a novel strategy for improving tumor treatment and, consequently, patient's quality of life. This review reports a broad overview about several aspects of magnetic hyperthermia addressing new perspectives and the progress on relevant features such as the ad hoc preparation of magnetic nanoparticles, physical modeling of magnetic heating, methods to determine the heat dissipation power of magnetic colloids including the development of experimental apparatus and the influence of biological matrices on the heating efficiency.

Fundamentals and advances in magnetic hyperthermia

The main advantage of confocal microscopes over their conventional counterparts is their ability to optically “section” thick specimens; the thin image slices thus obtained can be used to reconstruct three-dimensional images, a capability which is particularly useful in biological applications. However, it is well known that the resolution and optical sectioning ability can be severely degraded by system or specimen-induced aberrations. The use of high aperture lenses further exacerbates the problem. Moreover, aberrations can considerably reduce the number of photons that reach the detector, leading to lower contrast. It is rather unfortunate, therefore, that in practical microscopy, aberration-free confocal imaging is rarely achieved. Adaptive optics systems, which have been used widely to correct aberrations in astronomy, offer a solution here but also present new challenges. The optical system and the source of aberrations in a confocal microscope are considerably different and require a novel approach to wavefront sensing. This method, based upon direct measurement of Zernike aberration modes, also exhibits an axial selectivity similar to that of a confocal microscope. We demonstrate an adaptive confocal fluorescence microscope incorporating this modal sensor together with a deformable membrane mirror for aberration correction. Aberration corrected images of biological specimens show considerable improvement in contrast and apparent restoration of axial resolution.

https://www.pnas.org/content/pnas/99/9/5788.full.pdf

Adaptive aberration correction in a confocal microscope

Transform methods for image reconstruction from projections are based on analytic inversion formulas. In this tutorial paper, the inversion formula for the case of two-dimensional (2-D) reconstruction from line integrals is manipulated into a number of different forms, each of which may be discretized to obtain different algorithms for reconstruction from sampled data. For the convolution-backprojection algorithm and the direct Fourier algorithm the emphasis is placed on understanding the relationship between the discrete operations specified by the algorithm and the functional operations expressed by the inversion formula. The performance of the Fourier algorithm may be improved, with negligible extra computation, by interleaving two polar sampling grids in Fourier space. The convolution-backprojection formulas are adapted for the fan-beam geometry, and other reconstruction methods are summarized, including the rho-filtered layergram method, and methods involving expansions in angular harmonics. A standard mathematical process leads to a known formula for iterative reconstruction from projections at a finite number of angles. A new iterative reconstruction algorithm is obtained from this formula by introducing one-dimensional (1-D) and 2-D interpolating functions, applied to sampled projections and images, respectively. These interpolating functions are derived by the same Fourier approach which aids in the development and understanding of the more conventional transform methods.

Reconstruction algorithms: Transform methods

Presented in this paper is an optical implementation of a shift- and rotation-invariant pattern recognition technique. A computer-generated hologram is designed to match with one of the circular harmonic components of the target. Experimental results with simple photographic objects show that targets with different locations and orientations can be simultaneously recognized by the optical system.

Optical pattern recognition using circular harmonic expansion

The authors present a method of measuring the temperature of magnetic nanoparticles that can be adapted to provide in vivo temperature maps. Many of the minimally invasive therapies that promise to reduce health care costs and improve patient outcomes heat tissue to very specific temperatures to be effective. Measurements are required because physiological cooling, primarily blood flow, makes the temperature difficult to predict a priori. The ratio of the fifth and third harmonics of the magnetization generated by magnetic nanoparticles in a sinusoidal field is used to generate a calibration curve and to subsequently estimate the temperature. The calibration curve is obtained by varying the amplitude of the sinusoidal field. The temperature can then be estimated from any subsequent measurement of the ratio. The accuracy was 0.3 degree K between 20 and 50 degrees C using the current apparatus and half-second measurements. The method is independent of nanoparticle concentration and nanoparticle size distribution.

Magnetic nanoparticle temperature estimation

The Abel transform and its inverse appear in a wide variety of problems in which it is necessary to reconstruct axisymetric functions from line-integral projections. We present a new family of algorithms, principally for Abel inversion, that are recursive and hence computationally efficient. The methods are based on a linear, space-variant, state-variable model of the Abel transform. The model is the basis for deterministic algorithms, applicable when data are noise free, and least-squares-estimation (Kalman filter) algorithms, which accommodate the noisy data case. Both one-pass (filtering) and two-pass (smoothing) estimators are considered. In computer simulations, the new algorithms compare favorably with previous methods for Abel inversion.

Recursive methods for computing the Abel transform and its inverse

Significant improvement in the longitudinal (optical axis) resolution of a microscope has previously been obtained either by posterior digital processing of optical sections collected with a conventional microscope, or by collecting sections with a confocal scanning microscope. In this paper we report the feasibility of obtaining longitudinal resolution comparable to the lateral diffraction limit by posterior processing of confocal sections. A confocal through-focus image series was simulated numerically and restored by constrained iterative deconvolution and by maximum likelihood. Several typical imaging situations were simulated. The results support the possibility of achieving equal longitudinal and lateral resolution.

Enhanced 3-D reconstruction from confocal scanning microscope images. 1: Deterministic and maximum likelihood reconstructions.

The harmonics produced by the nonlinear magnetization of superparamagnetic nanoparticles have been utilized in a number of budding medical devices Here we expand on an earlier technique for quantitatively measuring nanoparticle temperature in a purely ac field by including the presence of a static field The ability to quantify nanoparticle temperature by tracking changes in the 4th/2nd harmonic ratio is presented and shown to achieve an accuracy of 079 K The advantage of even harmonics, issues with odd harmonics in the presence of a static field and the potential for future incorporation into an imaging system are discussed

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Nanoparticle temperature estimation in combined ac and dc magnetic fields.

The enhanced depth discrimination of a confocal scanning optical microscope is produced by a pinhole aperture placed in front of the detector to reject out-of-focus light. Strictly confocal behavior is impractical because an infinitesimally small aperture would collect very little light and would result in images with a poor signal-to-noise ratio (SNR), while a finite-sized partially confocal aperture provides a better SNR but reduced depth discrimination. Reconstruction algorithms, such as the expectation-maximization algorithm for maximum likelihood, can be applied to partially confocal images in order to achieve better resolution, but because they are sensitive to noise in the data, there is a practical trade-off involved. With a small aperture, fewer iterations of the reconstruction algorithm are necessary to achieve the desired resolution, but the low a priori SNR will result in a noisy reconstruction, at least when no regularization is used. With a larger aperture the a priori SNR is larger but the resolution is lower, and more iterations of the algorithm are necessary to reach the desired resolution; at some point the a posteriori SNR is lower than the a priori value. We present a theoretical analysis of the SNR-to-resolution trade-off partially confocal imaging, and we present two studies that use the expectation-maximization algorithm as a postprocessor; these studies show that a for a given task there is an optimum aperture size, departures from which result in a lower a posteriori SNR.

Enhanced three-dimensional reconstruction from confocal scanning microscope images. II. Depth discrimination versus signal-to-noise ratio in partially confocal images.

Eric W. Hansen

Papers

Magnetic nanoparticle temperature estimation

Recursive methods for computing the Abel transform and its inverse

Enhanced 3-D reconstruction from confocal scanning microscope images. 1: Deterministic and maximum likelihood reconstructions.

Nanoparticle temperature estimation in combined ac and dc magnetic fields.

Enhanced three-dimensional reconstruction from confocal scanning microscope images. II. Depth discrimination versus signal-to-noise ratio in partially confocal images.