Chapter V Applications of complex field encoding
V. 2 Microscopy
Finally, it is truly relevant the contribution of this type of techniques to microscopy due to its versatility [11]. In microscopy, SLMs can serve several purposes: they can be employed to control the illumination over the sample or in the imaging path, even both simultaneously. As this thesis is aimed to the generation of arbitrary complex fields, here we focus deeply on the use of SLMs for this purpose.
But prior to investigate different ways to take advantage of the complex field encoding on microscopy, it is worth commenting on some other uses where SLMs are employed to enhance the images recorded by a microscope or even to develop some new techniques. For instance, the ability of phase-only SLMs of controlling the phase at will enables the use of techniques that increases the image contrast. The main idea lies on the use of SLMs as Fourier filters. By placing a modulator properly in a certain configuration (i.e. at the Fourier plane of a 4f imaging system), it is possible to control the spatial frequencies, enabling the use of different contrast enhancing techniques. It is not difficult to find reports where a modulator is employed to improve the contrast of the images. Existing techniques can be adapted to be used with SLMs. This is the case of differential interference contrast [130]. Previously, this method use to employ Wollaston prisms to record two slightly displaced coherent images. These images are overlapped in a certain plane generating an interference pattern. The SLM substitutes these prisms to generate and overlap the two images of a sample. The ability of the SLM to vary dynamically the encoded masks allows changing the orientation, displacement, phase shift between images, and other parameters, enabling a fast acquisition of the interference patterns. In a similar way, under some conditions, placing the SLM in the Fourier plane of a focusing system allows to directly control the Fourier components of the beam. Blocking or shifting the zeroth-order Fourier component gives rise to different methods known as dark field microscopy or phase contrast microscopy, enabling several ways to obtain enhanced images [131].
Focused on situations in which SLMs are employed into the illumination path, but for tasks other than performing an irradiance shaping, we can find techniques like optical diffraction tomography (ODT) [132]. ODT is a technique based on illuminate a certain sample under several angles of incidence and detect the intensity of the diffracted far field from different points of observation. From this set of bi-dimensional images, it is possible to
reconstruct the three-dimensional distribution of the sample after a proper numerical procedure. To vary the inclination angle of the illumination over the sample, one can choose among different options including DMDs [133], galvanometric mirrors [134] or LC-SLMs [135].
Another improvement is related to aberrations correction. Several effects produced by the optical system can deform the point spread function (PSF) of the objective. Slight misalignments, dirt on the surface of the optical elements, or other unwanted situations can produce defocus or displacements on the focal spot, preventing from obtaining an ideal PSF for the illumination of a microscope. SLMs can correct it by encoding a phase mask designed to correct those aberrations [136,137]. Thus, they allow to generate arbitrary illumination patterns and even to change them dynamically to perform sequential measurements. Simultaneously, the beam shaping can be complemented with the correction of the aberrations to improve the irradiance pattern generated over the sample. Nevertheless, this ability to change the PSF not only can be employed to obtain an ideal focus, but also to gain advantage of specifically designed ones. For instance, a double helix PSF was demonstrated as a useful tool to obtain three-dimensional single- molecule fluorescence images beyond the optical diffraction limit [138]. Finally, due to the capability of modulators to control both amplitude and phase, SLMs are an excellent tool to control the irradiance (and phase) profile of the illumination over the sample. In this way, SLMs can be employed to encode DOEs able to perform some tasks. For instance, the precise control that SLMs provide about some physical parameters (e.g. amplitude and phase) allows controlling light propagation inside scattering media. This kind of materials generates a random scattering effect to the light that passes through them. This is mainly produced by non-uniformities present inside the whole volume of the medium. Experimentally, this effect hinders taking images of objects when a turbid media is involved. Recently, SLMs have been employed to pre-compensate the mentioned optical distortions improving the results obtained under these conditions. One of the first moves in that direction was done when focalization of coherent light through a deep layer of turbid media was demonstrated [139]. The main idea was to employ an SLM and a photo- detector in closed-loop configuration to find the phase mask that optimizes the desired output. Later, a crucial step was taken when it was demonstrated the possibility of measuring the transmission matrix of any turbid medium [140], enabling not only the spatial correction, but also the temporal distortions induced by scattering [141], and the polarization state of the light
after the medium [142]. The ability to generate a focal spot through these media is extremely relevant to achieve certain targets. For instance, if one is able to generate and displace a focus over a certain sample, it is possible to scan it. In that way, non-linear microscopy can employ these kind of techniques to recover images of a sample placed inside a turbid media [143]. But DOEs cannot only shape a single spot, but a set of them, even in different planes [144]. For instance, in this case the combination of Dammann lenses with gratings are employed to generate several 2D distributions in different planes, resulting in a 3D distribution of focus. A similar result can be obtained using a tuned version of the above-mentioned GSA. In [145], a hologram is designed to obtain multiple irradiance distributions located at different axial positions. These foci arrangements may be suitable to generate fluorescent effects to probe a 3D medium.
However, scanning techniques are known for their limited temporal resolution. In a single spot configuration, for each position of the focus, only one “pixel” of the retrieved image is obtained. Thus, to obtain the full image, a large amount of measurements should be performed. In fact, the higher the resolution, the higher the number of measurements needed to obtain it. The techniques reviewed in the previous chapters are perfect candidate to generate targeted illumination over a sample, speeding up the process. In last years, several techniques have been reported demonstrating, for instance, their usefulness to obtain fluorescence images of neurons, [26,146].
A different approach to obtain three-dimensional microscopic images is based on stereoscopy. The SLM is employed to generate a fringe pattern over the sample, and a detector is used to measure the deformed pattern caused by the surface of the sample [147,148]. Then, usually a computer is employed to calculate the image of the sample. However, unlike other techniques, this one relies on the surface of the sample to obtain the image. On the positive side, this allows to retrieve not only the image but also the topography of the sample. By contrast, this technique cannot deep into the sample. Moreover, as just a mere fringe pattern is needed on the illumination side, other amplitude-only systems as DMDs are being employed to fulfill the same function [149].
There are more applications in which SLMs are involved in one way or another to achieve a proposed objective or to improve the results but a complete list them all is beyond the scope of this thesis.
Finally, it is important to remark a couple of contributions published during the completion of this thesis. The first one proposes an arbitrary generation of multiple foci using the complex field encoding technique discussed in the previous chapter [117]. The second one employs the same technique to demonstrate, among other things, the possible application of the technique to nonlinear microscopy applications.