# Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display
###### Abstract  
We present in this paper a revision of three different methods we conceived in the framework of liquid crystal on silicon (LCoS) display optimization and application. We preliminarily demonstrate an LCoS self-calibration technique, from which we can perform a complete LCoS characterization. In particular, two important characteristics of LCoS displays are retrieved by using self-addressed digital holograms. On the one hand, we determine its phase-voltage curve by using the interference pattern generated by a digital two-sectorial split-lens configuration. On the other hand, the LCoS surface profile is also determined by using a self-addressed dynamic micro-lens array pattern. Second, the implementation of microparticle manipulation through optical traps created by an LCoS display is demonstrated. Finally, an LCoS display based inline (IL) holographic imaging system is described. By using the LCoS display to implement a double-sideband filter configuration, this inline architecture demonstrates the advantage of obtaining dynamic holographic imaging of microparticles independently of their spatial positions by avoiding the non-desired conjugate images. L 2018 8 2310 2018  
Note that LCoS displays can be configured to both operating in the amplitude-only or the phase-only regimes. Into the amplitude modulation scheme, output intensity distribution can be customized by properly modifying the polarization spatial distribution of the wavefront, and projecting it over a linear analyzer, being this configuration commonly used for imaging proposes. Conversely, LCoS displays operating in the phase-only regime are commonly used for phase modulation, being of interest in a wide number of applications, such as microstructure fabrication [6], holography [7; 8], biomedical applications [9], waveguide optics [10], optical switching [11], microparticle manipulation [12; 13], etc. To guarantee an optimal working performance in all those applications, LCoS must be previously calibrated and optimized. In particular, the phase-voltage relation and the LCoS surface homogeneity (flatness) are two important characteristics to be calibrated as they directly determine the performance of the generated phase distribution [14; 15; 16]. In this paper, we review a novel method able to provide both characteristics in a compact and feasible optical arrangement. The method is based on the use of diffractive optical elements (DOEs) self-addressed to the LCoS display to be optimized. Here, the term \"self-addressing\" means that the used DOEs are addressed to the same LCoS display to be calibrated, this leading to an auto-calibrating procedure. In particular, two DOEs are self-addressed: (1) a split-lens configuration [17; 18] to fulfil the phase-voltage calibration; and (2) a spot-array pattern (Shack-Hartmann, S-H, configuration [19; 20; 21]) to realize the surface profile measurement. For the phase-voltage calibration case, a diffractive two split-lens configuration is addressed on the LCoS, which is illuminated by coherent light. This configuration is equivalent to the [PERSON]'s double slit experiment, so the well-known fringes pattern is realized to a propagated plane. Later, by adding different constant phases (by driving different voltages) to one of the two split-lenses phase distributions, the fringes pattern is shifted in the transversal direction according to the added phase. Under this scenario, the LCoS phase-voltage relation is directly obtained by analyzing the interferometry pattern shift within each driven voltage. Here, we want to note that our interferometry-based technique demonstrates great advantage compared to other existing schemes. For instance, the method is able to take into account the unsatisfied time-fluctuation effect (also refereed as flicker effect [22]) that degrades the performance of LCoS, without requiring extra metrological set-ups (i.e., the system is self-calibrated).