Volumetric displays

Three-dimensional (3-D) display is an ultimate display technology. From the theaters to TVs at home, to naked eye mobile devices, 3-D displays [1-3] have been gaining popularity in our daily lives. In this chapter, we will outline the basic operation principles for generating depth perception, in order to reahze 3-D displays. Several types of 3-D display devices stereoscopic displays, autostereoscopic displays, integral imaging, holography, and volumetric displays are discussed. 

Volumetric displays [80,81] use voxels, pixels that use three-dimensional coordinates (x, y, z), to present image in space. Each voxel scatters or emits light as if the hght were coming from a real 3-D object. The key concept of a volumetric 3-D display system is to have the entire display volume filled with voxels that can be selectively excited at any desired locations. For most volumetric displays, it is difficult to have shadows, because they cannot generate black pixels. 

Figure 16.20 (a) A volumetric display system based on rotating LED array (b) The displayed 3-D... 

Figure 16.21 Schematic diagram of a volumetric display using multiple mini-projectors and a rotating screen. Reproduced with permission from Wiley.

A multi-planar volumetric display presents the volume by a stack of 2-D images at different depths. An example is shown in Figure 16.22 employing 20 polymer-dispersed liquid crystal... 

J. Wu, C. Yan, X. Xia,etaL, An analysis of image uniformity of three-dimensional image based on rotating LED array volumetric display system, SID Tech. Digest, 41, 657 (2010). 

W. Song, Q. Zhu, T. Huang, et al.. Volumetric display system using multiple mini-projectors, SID Tech. Digest, 44, 318 (2013). 

A. Sullivan, A solid-state multi-planar volumetric display, SID Tech. Digest, 34, 1531 (2003). 

Measurements based on the law of conservation of energy are of two main types. In phase change calorimetry the enthalpy of the reaction is exactly balanced by the enthalpy of a phase change of a contained compound surrounded by a larger reservoir of the same compound used to maintain isothermal conditions in the calorimeter. The latter enthalpy, the measurand, is often displayed indirectly through the change in the volumetric properties of the heat reservoir compound, e.g. ice/water. 

The critical datum is not a buret reading, as it was in the case of the volumetric method. Rather, the amount of iodine used is determined coulometrically by computing the coulombs (total current over time) needed to reach the end point. The coulombs are calculated by multiplying the current applied to the anode-cathode assembly (a constant value) by the total time (seconds) required to reach the end point. The modern coulometric titrator automatically computes the amount of moisture from these data and displays it. 

The adsorption isotherms of the elution part (first peak) were used to calculate the BET area [5] of both samples. The results of this calculation and of comparison measurements with a static volumetric device are displayed in table 1. 

Figure I 1.7. Variation of viscoelastic scaling factors with gas content for PS-C02 and PDMS-C02 systems. Lower scaling factor values for PS-C02 system, compared with PDMS-C02 system, are due to the closer proximity of the experimental temperatures to Tg of the pure polymer. The top curve displaying results for iso-free volume dilution of high-Mw polystyrene by low-Af polystyrene represents the effect on viscosity of volumetric dilution of high-Mw chains. Viscosity reductions for polymer-gas systems are significantly lower than the iso-free volume dilution curve, indicating that viscosity reduction is primarily due to free volume contributed by dissolved gas.

For laboratory-scale modification, distinction has to be made between static and dynamic adsorption procedures. In a static procedure, the substrate is contacted with a known volume of gas at a well-defined pressure. The modifying gas may be stationary or circulating in a closed loop. Modification in a static gas adsorption apparatus allows the careful control of all reaction parameters. Temperature and pressure can be controlled and easily measured. Adsorption kinetics may be determined by following the pressure as a function of the reaction time. Figure 8.13 displays a volumetric adsorption apparatus, in which mercury is used, as a means to change the internal volume and for pressure measurement. 

In sediments and the maflc portion of the subducted crust, all of the reactions involving hydrous phases and carbonates involve solid solutions whose compositions depend on the bulk composition, in addition to pressure and temperature. Different bulk compositions cause different phase compositions and thus cause reactions to shift in P-T space, i.e., to start shallower or deeper. In peridotites, amphibole and to some extent chlorite are controlled by continuous and discontinuous reactions however, the other volumetrically important hydrous phases (e.g., brucite, serpentine, talc, and phase A ) in altered harzburgites display a relatively restricted compositional range, at least compared to those present in mafic eclogites. As a result, breakdown reactions of hydrous phases in harzburgites are dominated (in a first approximation) by discontinuous reactions, and take place over a restricted depth range of only a few kilometers. 

Very interestingly, Harding ound that the compressive strengths of polyurethane and polystyrene foams in one case and of polyurethane and phenolic foams in another case display the same dependence on the height-to-width ratio over a range from 1/2 to 2/1, despite the fact that the volumetric weights of these materials are... 

Graphical methods can be used to obtain the conversion from a series of reactors and have the advantage of displaying the concentration in each reactor. Moreover, no additional complications are introduced when the rate equation is not first order. As an illustration of the procedure consider three stirred-tank reactors in series, each with a different volume, operating as shown in Fig. 4-13<7. The density is constant, so that at steady state the volumetric flow rate to each reactor is the same. The flow rate and reactant concentration of the feed Q and Cq) are known, as are the volumes of each reactor. We construct a graph of the rate of reaction r vs reactant composition. The curved line in Fig. 4- 3b shows how the rate varies with C according to the rate equation, which may be of any order. 

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