Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display

Abstract

We apply the polar decomposition of the Mueller matrix describing a liquid-crystal-on-silicon display to identify the diattenuator, depolarizer, and retarder contributions as a function of the gray level. The retarder contribution is expressed in terms of the equivalent Jones matrix to apply previous techniques to evaluate the phase modulation. This allows searching for optimized polarization configurations for phase-or amplitude-only modulation responses. We present results for = 633 nm showing a phase-only modulation up to 2 rad and flat intensity modulation. © 2008 Optical Society of America OCIS codes: 230.3720, 230.6120, 260.5430. Liquid crystal displays (LCDs) have found widespread use as spatial light modulators (SLMs) in applications such as optical image processing, holographic data storage, programmable adaptive and diffractive optics, and optical metrology. For all these applications, their configuration as phase-only SLMs is very important to obtain high values of the diffraction efficiency [1]. This situation is achieved when the input and output polarization configurations are properly selected [2]. In recent years new liquidcrystal-on-silicon (LCoS)-based displays have attracted considerable interest due to their high resolution and excellent fill factor [3]. They are reflective displays that, due to the double pass through the device, allow for an increased phase modulation depth compared to previous twisted nematic (TN) LCDs. Several methods have been proposed to evaluate and predict the phase modulation for different polarization configurations. They usually employ the Jones matrix formalism [4,5], since the complex (amplitude and phase) modulation can be directly evaluated. However, the Jones formalism does not account for such other important polarimetric parameters as diattenuation and depolarization. For that purpose, the Mueller matrix formalism provides an alternative description. This approach is especially relevant to show evidence of a certain degree of depolarized light in the displays [6][7][8]. The Mueller approach has also been used to find LCD configurations leading to a phase-only modulation. For instance, Pezzaniti and Chipman [9] measured the Mueller matrix of a TN-LCD and calculated its average eigenpolarization states. More recently, the trajectory on the Poincaré sphere and its modification with external wave plates has also been employed with a TN-LCD [10]. These methods very elegantly and efficiently lead to a constant intensity configuration, but the phase modulation cannot be evaluated a priori and has to be measured. However, the possibility of predicting the phase-modulation is very desirable, since the phasemodulation depth can be increased in configurations with flat but no maximum intensity modulation [11].In this work we combine the Mueller and Jones approaches to perform a complete characterization of a LCoS display. We use results of a previous polarimetric characterization of the display based on the Mueller matrix approach [8], which showed up to 10% of th...

Influence of the incident angle in the performance of Liquid Crystal on Silicon displays

“…In order to extract more information from the Mueller matrices, we have used the combined method exposed in [11], where the Lu-Chipman polar decomposition [14] (based on the polar decomposition theorem [17]) is applied to the LCoS Mueller matrix. In this sense, the Mueller matrix of any depolarizing element can be expressed as the product of three Mueller matrices: the depolarizer, the retarder and the diattenuator matrices.…”

“…Because of this depolarization effect, the Mueller-Stokes (M-S) formalism has been adopted for LCoS displays, and a protocol to optimize the intensity [7] and phase [11] modulation responses has been developed. By extension, this protocol is valid to characterize any polarizing or depolarizing optical element.…”

Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics

“…This can be easily achieved in parallel aligned displays by selecting the input beam linearly polarized in the orientation of the LC molelcular director. In twisted nematic displays, phase-only modulation is obtained by using the appropriate elliptical polarization configuration [12][13][14]19].…”

“…In Ref. [19], the polar decomposition [23] of the characterized Mueller matrix for the LCoS was applied. In this sense, the Mueller matrix of the LCoS display is decomposed as the product of three Mueller matrices: a depolarizer, a retarder and a diattenuator.…”

“…However, the above mentioned depolarization effects led to the use of the Mueller-Stokes formalism in the study of LCoS displays [5][6][7]. We have recently combined both types of analysis to evaluate the depolarization as well as to find polarization configurations that lead to an amplitude-only or to a phase-only modulation [19].…”