\documentclass[a4paper]{article}

%To get rid of the stupid margins
\usepackage{fullpage}

\usepackage[utf8]{inputenc}
\usepackage{amssymb,amsmath}
\usepackage[section]{placeins}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{subcaption}

% To use the Palatino font for text
\usepackage{mathpazo}
% To use Euler font for mathematical formulae
\usepackage{euler}

\newcommand{\al}{\alpha}
\newcommand{\la}{\lambda}
\newcommand{\da}{\delta}
\newcommand{\Da}{\Delta}
\newcommand{\be}{\beta}
\newcommand{\sa}{\sigma}
\newcommand{\ta}{\theta}
\newcommand{\D}{\,\mathrm{d}}
\newcommand{\Fin}{F}
\newcommand{\pict}[1]{\includegraphics[width=5m]{#1}}

%\begin{figure}[h]
%\centering
%\includegraphics[width=linewidth]{}
%\caption{}
%\label{}
%\end{figure}

\author{V.~Maioli}
\title{Fluorescence Tomography}
\date{}

\begin{document}

\maketitle


\section{Introduction to fluorescence microscopy}
% Only 2-3 pages long

Fluorescence microscopy is a key tool for actual research in biology and medicine. Its ability to provide full contrast - only fluorescent labelled object are imaged - is one of the reasons for this.

\subsection{Physical principles of fluorescence}

Fluorescence occurs when a species (for example, atom or molecule) is excited by light at a particular wavelength and then return to a lower energy level by emitting light.

Schematically, a species presents a series of electronic energy states, completed by rotational and vibrational sub-levels.

When excited, a species will be brought up on any energy level corresponding with the excitation wavelength, but then will decay non-radiatively to the corresponding electronic state from which radiation will occur.

The fluorescence is characterised both by the absorption and the emission spectrum. These correspond to which wavelengths can be absorbed or emitted by the species, and with which `efficacy`.

These spectra have the important properties that the peak of absorption (in frequency) is of higher value than the peak of emission, which is called the Stokes shift and is caused by the non-radiative decrease of energy before the actual light emission; and that the emission spectrum is symmetrical to the absorption spectrum.

\subsection{Fluorescence microscopy techniques}

The Stokes shift is what enables the principle of a fluorescence microscope : if the absorption and emission spectra are well separated, then a simple dichroic beam splitter can separate the excitation to image only the emitted light.

A particularly interesting technique to study biological processes is the Forster resonant energy transfer, or FRET, which modifies the fluorescence wavelength when two fluorophores are close enough.

The easiest way to image is to use direct measurements of the fluorescence intensity. In this case, analysis would be based on the respective proportion of different fluorophores, for example in FRET situations, or with two different fluorescent labels.

Another technique is to use measurements of the lifetime of the fluorescence, which is called FLIM (fluorescence lifetime imaging). This can distinguish between, for example, to fluorophore of mostly same colour, and should provide an intensity-free measure of the presence of a fluorophore.
A variant exists where the excitation light is modulated sinusoidally in intensity; due to the lifetime of decay the fluorescence responds with a given phase shift which can be measured.

\section{Optical sectioning}
% Main bulk of text, 10 pages ? say 15

In conventional (wide-field) microscopy, imaging of thick samples is hindered because of the scattered and out-of-focus contributions to the illumination which forbid to isolate the plane of interest. A number of techniques have thus developed to be able to image in three dimensions and inside a sample, allowing to work on non-sectioned samples, and in particular on live samples - which still have to be transparent to the wavelengths used.

% [STED ?]
% [4$\pi$ ?]

% !!! /!\ LSM = laser [point] scanning [confocal] microscope, by Zeiss != light sheet microscopy

\subsection{Confocal microscopy}

The aim of confocal microscopy is to get rid of all unwanted background light. This is realized by illuminating the sample with light from a pinhole, generating a single point inside the sample which is the optical conjugate of the source pinhole. The detector pinhole is another conjugate to the sample, and as such, any light passing through the detector pinhole, must be coming from the sample point. Effectively, this system rejects most of out-of-focus light.

In this situation, the actual point-spread function of the microscope is the product of the PSFs of the two pinholes, which reduces the overall full width at half maximum and improves the overall resolution.

The confocal microscope has been a momentous event in optical microscopy, and may have been one of the real improvements over the XVIIth century microscopes.

	\subsubsection{spinning disk confocal microscopes}
	The spinning disk versions of the confocal microscope make use of a disk patterned with a series of pinholes. In the original design, the holes used to illuminate the sample and the ones used to collect light from it were diametrically opposite and identical. 

	Each couple of hole works as an individual confocal microscope, and the rotation of the disk enables the scanning of the whole image.

	Further iterations of the concept ('one-sided') used the same set of holes for illumination and detection, making use of a device to separate both paths of light.

	Still, common to these forms of spinning disk is a very poor light collection, as most of it is not passing through the pinholes. As a results, they are mainly used for reflection imaging (when it is the reflected light from the sample which is recorded) rather than fluorescence imaging.

	A useful improvement one the one-sided design is the use of a micro-lens array to focus the laser onto the pinholed disk, for example the Yokogawa scanning system] It gives a much better light efficiency and is the basis of most commercial spinning-disks actually. 
	
	A fundamental limitation of spinning-disk is the inevitable cross-talk between holes: light incoming from one pinhole and reflected (or triggering fluorescence) can be caught by another pinhole and reduce the confocality.

	\subsubsection{slit-scanning confocal}

	In \cite{Woll06}, a straightforward upgrade of the confocal microscope to a line-scanning version is made. It involves the generation of a sheet of light, which is then shone to the sample, creating a line of illumination, which is imaged by the same lens and recorded by a line-shaped CCD. Again, a 'pinhole' (here, rather, a slit) is used to reject out-of-focus light.

	This version of confocal microscopy has as a plus side a better speed of operation, to the price of losing some confocality as out-of-focus light can enter the detector along the slit opening.
	
	Another version uses an another slit to create the light sheet rather the slit-coated mirror, with reduced performances (mostly due to the imperfections of the slit itself).
	
\subsection{Multiphoton microscope}

The multiphoton microscopy is a variation on the fluorescence principle. In standard fluorescence, a photon of frequency $\nu$ triggers a corresponding upward transition in the species. In $n$-photon fluorescence, this same transition is triggered by radiation at frequency $\frac\nu n$. This is much more unlikely, and so requires much more power to occur than usual fluorescence. It is a non-linear optical process, as theoretically the intensity of fluorescence will depend on the square of the illumination intensity.

One advantage is that it is then possible to use longer wavelengths of illumination.

Another advantage is the intrinsic sectioning effect. Indeed, as more power is needed, the two-photon effect will occur only in the focal region, where most light is concentrated. That is, only the focal region will fluoresce.


Other non-linear processes such as second harmonic generation from non-centrosymmetric, crystalline structures are also used in microscopy, still not specifically for optical sectioning as they have pretty specific applications.

\subsection{Structured Illumination}

The structured illumination technique casts light through a pattern (such as a grating) onto the object, and by varying the pattern computes the axial component. 

A mask is mounted in the optical path, patterned with a grating, and then multiple images are taken while shifting the mask. The images are then combined to give the final, resolved image.



HiLo is a variation on the structured illumination, where the structure is given by the laser's speckle (non-focused interference pattern).



% [TIRF ?]

\subsection{Light Sheet Microscopy}

Cf. \cite{Huisken09},  \cite{Dodt07}

The light sheet microscopy takes another approach, which is to illuminate only the part of interest in the sample. 

The light sheet microscopy, often called single plane illumination microscopy, aims at optically section a specimen by illuminating only a fine sheet of light created by a cylindrical lens which focuses the light in only one direction, and then imaging in the perpendicular direction.

	\subsubsection{Ultramicroscopy}
	One of the first occurrences of the idea of imaging with a sheet of light arose at the beginning of the XXth century under the name ultramicroscopy, for the use with dark field imaging.

	% 1901

	\subsubsection{Single plane illumination microscopy}
	
One of the first modern-day presentation of a light-sheet technique is \cite{Huisken04}.


	% highly oriented, etc.

Still, imaging in thick samples can prove difficult, as fluorescence light can be scattered in the way back to the objective. To address this specific problem, confocal 'light sheet' microscopes have been designed, for example in \cite{Silvestri12}. They are rather variations on the line-scanned, and very close in their principle to a confocal line-scanning microscope, except that the illumination is coming from the side, as in PSIM, while in slit-scanning confocal as done by Zeiss, illumination is done by a sheet of light coming in the front.  The light-pencil scanning process allows for less light being dispensed to the sample than in a light-sheet slit-scanning confocal microscope. A laser beam is shot at the sample and an image is recorded in the  orthogonal direction; and the beam is scanned through all the sample to acquire the three-dimensional image.

	\subsubsection{Oblique Plane microscopy}
	Cf. \cite{Dunsby08}, \cite{Kumar11}
	
	In oblique plane microscopy, a single lens is used both for the illumination and the imaging of the sample. For this purpose, a high NA objective is needed, and the light will illuminate an oblique sheet inside the sample.
		
		% [The image relay]
	
	Another objective is then used to image the plane at the right angle, to avoid aberrations related to imaging tilted image. This requires a complex set-up of three microscopes; as well as two camera to image fluorescence and one for conventional bright-field image.
	

% [Optical coherence tomography ?]


	
\subsection{OPT}

Cf. \cite{Sharpe02}, \cite{McGinty11}

	The optical projection tomography is the adaptation of the principle of the X-ray computed tomography. A collimated beam is shot at the sample (which must be mostly transparent at the wavelength used) and the transmitted light is recorded. This light correspond to the line integral of the various absorption along the optical path; the corresponding attenuation for a ray along direction $s$ is $\rho = \int_s \mu(x,y)\D s$.
	
	Such a line integral (an integral along a path in 2D) can be rewritten with Kronecker deltas as \[\rho(r,\ta) = \int_{-\infty}^\infty \int_{-\infty}^\infty \mu(x,y)\da(x\cos\ta+y\sin\ta - r)\D x\D y\] and is called a \emph{sinogram}. This is called a Radon's transform and a number of numerical algorithms to invert it are used, most of which can be categorized as filtered back-projection or iterative reconstruction.
	
% [Radon transform]

\subsection{OCT}

In OCT, a light to temporal low cohrence is used in a set-up alike to a Michelson microscope with the sample in one of the arms, to give interference only on specific reflective points in the sample.

\subsection{Other sectioning techniques}

A very precise technique to image a very thin plane is the total internal reflection microscope (TIRF), where a light experiences total reflection on the sample, giving rise to an evanescent wave in it.

However, this can not be used for 3D imaging, as only a very small part of the sample, just under the coverslip, is imaged.

% near-field microscope?

\section{Applications of OPM}

\subsection{Biological situation}
% 2 - 3 pages max

% \begin{figure}[h]
% \centering
% \includegraphics[width=\textwidth]{setup}
% \caption{Schematic of the He-Ne laser cavity}
% \label{setup}
% \end{figure}

	\subsubsection{Calcium sparks, transverse tubules}
	
	\subsubsection{Microscopes commonly used to image sparks in cardiomyocites}
\subsection{Computational aspects}
	Sparks detection
	T-tubules modulation depth calculation
	Shearing and resampling of an OPM volume
	
\section*{Conclusion}

no super resolution

% 2 pages
%\nocite{*}
\bibliographystyle{plain}
\bibliography{master}

\end{document}
