Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
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We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
IntechOpen is proud to announce that 179 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\n
Throughout the years, the list has named a total of 252 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\n
We wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
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\n\t\t\t
1. Introduction
\n\t\t\t
In the last decade solar photovoltaic (PV) systems have become available as an alternative electrical energy source not only in remote locations but even in densely populated areas as their price decreases and their performance increases. The chapter discusses fixed PV array potential in Slovenia with great geographical and topographical variety, which is a reason that the climate, and also PV potential, changes rapidly already on short distances. The study is based on the meteorological measurements of solar irradiance, air temperature and albedo from the MODIS satellite data. Simulations for four meteorological stations were employed to determine combinations of azimuth and tilt angle for fixed PV arrays that would enable their maximum efficiency. As expected, large tilt with southern orientation is optimal during winter and almost flat installations are optimal during summer. The optimal PV gains are compared also with the results obtained by using the rule of a thumb tilt angle showing some significant differences in some cases.
\n\t\t
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2. Theoretical background
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PV system users can define the orientation of their PV arrays: their azimuth angle (angle measured clockwise from North) and the tilt angle (the angle above the horizontal plane). Previous studies show that, if local weather and climatic conditions are not considered, the optimal fixed tilt angle of PV modules depends only on geographical latitude φ (and the optimal azimuth is always south in the northern hemisphere). Considering only direct solar irradiation, the optimal tilt angle during the year can be calculated as φ - δs, where δs is the declination of the Sun. For example, for latitude φ = 46º N the maximal direct irradiation on 21 March and 21 September is achieved at a tilt angle of 44º. On 21 June and on 21 December the tilt angle is changed by the declination of the sun (± 23.5°) to 20.5° and 67.5º.
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Due to the diffuse light the optimal tilt angles differ from those in reality. Since modules are frequently incorporated into the architecture of some objects, often some “rule of thumb” is applied. By taking such an approach a certain “yearly optimum” is obtained – as suggested by Duffie and Beckman (1991) – the tilt angle should be 10º–15º more than the latitude during winter and 10º–15º less than the latitude during summer. The lower values are originally based on the classical report by Morse & Czarnecki (1958) from the mid-20th century. Their suggestion for the annually optimally fixed tilt angle is a value 0.9 times the latitude, which results in 40º for Slovenia. Other authors (Lewis, 1987; Heywood, 1971; Lunde, 1982; Garg, 1982) have concluded that the optimal tilt differs from the latitude in a range between ±8º and ±15º. An analytical equation to find the daily optimal tilt angle at any latitude has also been used (El-Kassaby & Hassab, 1994). For example, the average optimal tilt angle on Cyprus (latitude φ = 35ºN) equals 48º in the winter months (φ + 13º) and 14º (φ – 21º) in the summer months (Ibrahim, 1995). The optimal tilt was estimated for Brunei Darussalam on the basis of maximising the global solar irradiation reaching the collector surface for each month and year (Yakup & Malik, 2001). The tilt optimised for winter in Poland equals 50º–65º, for summer 10º–25º, and the PV module does not necessarily have to be oriented directly to the south – a range in the azimuth angle of -60º to +60º from the South also provides good results (Chwieduk & Bogdanska, 2004). The optimal tilt angle in Turkey varies from 13º–61º from summer to winter (Kacira et al., 2004), while the monthly optimised tilt in Ireland can vary from 10º to 70º (Mondol et al., 2007).
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The optimal tilt for the whole of Europe (PVGIS) shows that climate characteristics have a huge influence on the optimal tilt (Huld et al., 2008). In this contribution we particularly emphasise local weather and climatic conditions when computing the optimal orientation and tilt. As we will show in Section 3, these may differ considerably from the “maximum noon direct irradiation” as well as from the “rule of thumb” results.
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2.1. Solar irradiance on a tilted plane
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The most important parameter for computing the solar irradiance reaching the Earth’s surface is cloud coverage. In clear-sky conditions the next most important factor is the optical path length as the transmissivity of the atmosphere exponentially depends on it, which implies the position of the Sun in the sky (its zenith angle \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tϑ\n\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and azimuth A\n\t\t\t\t\t\n\t\t\t\t\t\tS\n\t\t\t\t\t that may be aggregated into unit vector \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tϑ\n\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\ttowards the Sun) changing over the course of a day and year. The true solar time (considering the geographical latitude and the equation of time) has been used for accurate computations and not the zonal time.
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Actual irradiance on the tilted plane varies significantly with its orientation geometry (tilt τ – angle of inclination between the horizontal surface and the PV module’s receiving plane, and orientation A – the azimuth angle between the North and the azimuthal component of the normal to the PV’s plane; both may be aggregated into a unit normal vector of the plane\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t→\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\tA\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t.
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Solar irradiance is usually measured on a horizontal plane as global irradiance E\n\t\t\t\t\t\n\t\t\t\t\t\tgl\n\t\t\t\t\t. The direct component E\n\t\t\t\t\t\n\t\t\t\t\t\tgl, dir\n\t\t\t\t\t and diffuse component E\n\t\t\t\t\t\n\t\t\t\t\t\tgl,diff\n\t\t\t\t\t of global irradiance must be considered separately because of their very different dependences on the tilted irradiance. When knowing the two components one can compute irradiance E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t on the tilted plane (in the meteorological community this is called quasi-global irradiance). The effect of the PV module’s tilt and azimuth angle on the direct part of solar tilted irradiance E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt,dir\n\t\t\t\t\t is described by a scalar product of the two unit vectors:
The effect of diffuse tilted irradiance (E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt,dif\n\t\t\t\t\t) can only be considered to be isotropic when there are no obstacles (e.g. mountains, buildings) on the horizon and the whole sky is covered by clouds of uniform brightness (Fig. 1). Many anisotropic models have therefore been developed: e.g. Brunger & Hooper (1993); a good overview is included in Kambezidis et al. (1994) but they mostly have an empirical background and thus their use is only suitable when a calibration of the model with measurements on the tilted surface is possible. Therefore, simplified isotropic models based on the parameter called the sky-view factor (svf) are mostly used. The sky-view factor is defined as the hemispherical fraction of unobstructed sky. There are several isotropic models of svf for inclined receivers. The 2D one: svf = (1 + cos τ)/2 (Mondol et al., 2007; Huld et al., 2008; Liu & Jordan, 1963), the improved one with a more realistic 3D consideration: svf = (1 + cos\n\t\t\t\t\t\n\t\t\t\t\t\t2\n\t\t\t\t\t τ)/2 (Badescu, 2002; Brunger & Hooper, 1993), as well as the 3D linear model by Tian et al. (2001):
Besides diffuse radiation from the sky, reflected (multiple scattered) radiation from the ground can also be important, especially for modules with a larger tilt and in areas of high ground reflectivity, like in a snow-covered landscape. Ground reflection is defined by the ground-view factor (gvf) that is a complementary parameter to the sky-view factor:
a) 3D approach to estimating the sky-view factor – the visible sky is limited by the horizontal plane and tilted plane of the PV module, thus only that part of the hemisphere between these planes is visible.
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For the diffuse irradiation coming from the ground is beside the geometry important also the ground reflectivity, characterised by the albedo (reflectivity) of the surrounding surfaces a\n\t\t\t\t\t\n\t\t\t\t\t\tgr\n\t\t\t\t\t. A constant albedo of 0.2 (typical grassland) was used in most previous studies. Some other approaches as Gueymard (1993) also suggest a seasonal albedo model. Such an albedo changes over the year according to the latitude and land cover of the observed area or to anisotropic approaches (Arnfield, 1975). These models are mainly appropriate for areas where a direct reflection is possible.
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Tilted solar irradiance E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t of a tilted plane is written by many authors as the sum of the abovementioned contributions. The diffuse component coming from the sky decreases with the tilt angle while at the same time the ground diffuse part of the irradiance increases:
Just recently the first two authors of this contribution have elaborated a more exact and conceptually proper approach based on the integration of isotropic radiance of sky L\n\t\t\t\t\t\n\t\t\t\t\t\tsky\n\t\t\t\t\t that gives, when integrated over the whole hemisphere, the diffuse irradiance of horizontal receiving surface E\n\t\t\t\t\t\n\t\t\t\t\t\tgl,dif\n\t\t\t\t\t\n\t\t\t\t\t= π L\n\t\t\t\t\t\n\t\t\t\t\t\tsky\n\t\t\t\t\t. Integration over the hemisphere, for which part of it has the radiance of sky L\n\t\t\t\t\t\n\t\t\t\t\t\tsky\n\t\t\t\t\t and the other part has a different radiance of ground L\n\t\t\t\t\t\n\t\t\t\t\t\tgr\n\t\t\t\t\t results in irradiation of the tilted surface E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t. If the albedo a\n\t\t\t\t\t\n\t\t\t\t\t\tgr\n\t\t\t\t\t and the coefficient k describing the contribution of the diffuse irradiation to the global irradiation (E\n\t\t\t\t\t\n\t\t\t\t\t\tgl,dif\n\t\t\t\t\t = k E\n\t\t\t\t\t\n\t\t\t\t\t\tgl\n\t\t\t\t\t) are also considered, an alternative, more accurate estimate of irradiation of the tilted receiving surface is obtained:
Expressions (4) and (5) differ only as regards diffuse irradiation; the difference depends on reflectivity a\n\t\t\t\t\t\n\t\t\t\t\t\tgr\n\t\t\t\t\t and on contribution k of the diffuse irradiance to the global irradiance. For example, for a\n\t\t\t\t\t\n\t\t\t\t\t\tgr\n\t\t\t\t\t = 0.2 and k = 0.5 the results differ by up to approximately ±6% for the diffuse irradiance, and up to approximately ±3% for the whole irradiance of tilted irradiance E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t. Here a more appropriate expression (5) was applied; more details about this are found in a submitted paper (Rakovec & Zakšek, n.d.).
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2.2. Performance of PV modules and arrays
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The energy conversion efficiency of a PV module or array as a group of electrically connected PV modules in the same plane is defined as the ratio between electrical power P\n\t\t\t\t\t\n\t\t\t\t\t\tPV\n\t\t\t\t\t conducted away from the module, and the incidence power of the sun: P\n\t\t\t\t\t\n\t\t\t\t\t\tPV\n\t\t\t\t\t\n\t\t\t\t\t(t)/SE\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t\n\t\t\t\t\t(t) = η. Normally, their efficiency is defined under standard test conditions η\n\t\t\t\t\t\n\t\t\t\t\t\tSTC\n\t\t\t\t\t (STC – module temperature: T\n\t\t\t\t\t\n\t\t\t\t\t\tSTC\n\t\t\t\t\t = 25º C, irradiance: E = 1000 W/m2, spectrum: AM1.5; IEC 61836-TR/Ed.2:2007; IEC 60904; http://www.iec.ch). The output power of a PV module depends on several parameters, including the irradiance, incidence angle and PV cell temperature T as the most influential. Namely, the PV cell efficiency also depends on its temperature as in solar cells based on the p-n junction diode principle the efficiency decreases with increasing temperature due to the higher dark current (Green, 1982). The efficiency temperature dependence is normally expressed by a linear equation:
The value of γ is approximately -0.004/K for polycrystalline silicon cells and modules (Carlson et al., 2000).
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Beside the irradiance, incidence angle and temperature dependence of the PV module, the output power of the PV system also depends on system losses: Joule losses in wirings of PV modules into PV arrays and inverter losses. These additional losses do not influence the tilt and azimuth dependence of the output energy since they only depend on the output power and on irradiance and not on time like the module\'s temperature. To obtain the system energy output from the PV module output energy we used a typical system performance factor of 85% in our study.
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2.3. Thermal model of PV modules
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How the temperature of the absorbing material of the receiving PV module increases depends on the energy exchanges between the absorber and its environment. Different assumptions can be made as regards the PV module energy balance equation. To explain only the basic energy exchange here we consider the PV module as a whole: cells with temperature T\n\t\t\t\t\t\n\t\t\t\t\t\tc\n\t\t\t\t\t, the covering plate with its temperature T\n\t\t\t\t\t\n\t\t\t\t\t\tp\n\t\t\t\t\t, eventually with the temperature on the surface (where it exchanges energy with the environment) also different from the one on the inner side of the plate are all considered to be one object with temperature T and with heat capacity c, having mass m and a receiving area S. Such a simplification neglects all the energy flows between the separate parts of the PV module, but on the other hand emphasises only the most important features of PV module energetics, without entering into particular details. In this paper we will also focus only on outdoor conditions. We also suppose, again to simplify the explanation, that all the surroundings have the same temperature as environmental air T\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t. In principle, for both PV modules and solar thermal (ST) solar collectors the energy flows are the same (Petkovšek & Rakovec, 1983). The divergence of all these energy flows results in cooling (normally during the late afternoon and night), while convergence (i.e. negative divergence) results in a warming of the absorber (normally during morning and early afternoon hours). The result expressed as (mc)dT/dt can be written as:
The terms in the equation are as follows: absorbed solar power Ps = (1-a)SE\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t, the (turbulent) convective heat exchange between the absorber and its atmospheric environment P\n\t\t\t\t\t\n\t\t\t\t\t\tconv\n\t\t\t\t\t\n\t\t\t\t\t= -K\n\t\t\t\t\t\n\t\t\t\t\t\tconv\n\t\t\t\t\t\n\t\t\t\t\t(T – T\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t\n\t\t\t\t\t), heat conduction between the absorber and the surrounding neighbouring parts of the module (e.g. supporting) P\n\t\t\t\t\t\n\t\t\t\t\t\tcond\n\t\t\t\t\t\n\t\t\t\t\t= -K\n\t\t\t\t\t\n\t\t\t\t\t\tcond\n\t\t\t\t\t\n\t\t\t\t\t(T – T\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t\n\t\t\t\t\t), the infrared radiation energy exchange (in the “terrestrial” wavelengths interval, centred at about 10 μm) P\n\t\t\t\t\t\n\t\t\t\t\t\tIR\n\t\t\t\t\t\n\t\t\t\t\t= Sε(ε\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t\n\t\t\t\t\tσT\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t – σT\n\t\t\t\t\t\n\t\t\t\t\t\t4\n\t\t\t\t\t\n\t\t\t\t\t), eventually latent heat exchanges, due to condensation or evaporation at the module, due to precipitation falling upon it etc: P\n\t\t\t\t\t\n\t\t\t\t\t\tlat\n\t\t\t\t\t and, of course, the flow of energy away from the absorber – the yield of the useful energy P\n\t\t\t\t\t\n\t\t\t\t\t\tPV\n\t\t\t\t\t. For the meaning of some of the symbols, see the main text; the others are: a – albedo of the module for solar radiation, S – the area of the module, K\n\t\t\t\t\t\n\t\t\t\t\t\tconv\n\t\t\t\t\t and K\n\t\t\t\t\t\n\t\t\t\t\t\tcond\n\t\t\t\t\t are the heat exchange coefficients, σ is the Stefan-Boltzmann constant and ε and ε\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t are the IR emissivities of the module and its environment, respectively. As regards the IR irradiation from above: for clear sky is IR emissivity ε\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t of approximately 0.7, while for overcast sky it approaches one – the emissivity of the black body.
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An analytical solution of equation (7) needs input data in analytical form; the two most important forms of environmental data are tilted irradiance E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t and environmental (air) temperature T\n\t\t\t\t\t\n\t\t\t\t\t\tenv\n\t\t\t\t\t. The climatological values exhibit an excellent similarity to the sinusoidal course and the same similarity is found for individual cases (see the example for Etilt in Fig. 3a) as shown in Fig. 2. But an equation in which some other coefficients also change in time differently from case to case can only be precisely integrated numerically for each of the governing conditions to give T(t) and with that also η[T(t)]. The numerical approach is used to calculate PV characteristics – and η[T(t)] – on the basis of the measured data.
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For example, an increase in the module\'s temperature from the morning hours until noon ΔT ≈ 47 K (Fig. 3d) leads to a negative relative change in the module\'s conversion efficiency γ ΔT = Δη / η\n\t\t\t\t\t\n\t\t\t\t\t\tSTC\n\t\t\t\t\t ≈ -0.19, which is confirmed with measurements (η = 10% at noon in Fig. 3c compared to η\n\t\t\t\t\t\n\t\t\t\t\t\tSTC\n\t\t\t\t\t\n\t\t\t\t\t= 12.3%).
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Figure 2.
Quasi-global solar irradiance fitted with a section of the sinusoidal function E\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ttilt0\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t+ E\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ttilt1\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\tsinω(t – t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t) (with E\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ttilt0\n\t\t\t\t\t\t\t = 405 W/m2, E\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ttilt1\n\t\t\t\t\t\t\t = 572 W/m2, ω = 8.46 h-1). The correlation coefficient between the data and the analytical function is 0.996.
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2.4. Some experimental results
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The Laboratory of Photovoltaics and Optoelectronics at the Faculty of Electrical Engineering of the University of Ljubljana (latitude: 46.07ºN, longitude: 14.52ºE) continuously monitors outdoor conditions of several variables and parameters relevant for PV (Kurnik et al., 2007; Kurnik et al., 2008), including E\n\t\t\t\t\t\n\t\t\t\t\t\ttilt\n\t\t\t\t\t, P\n\t\t\t\t\t\n\t\t\t\t\t\tPV, module temperature T and air temperature T\n\t\t\t\t\t\n\t\t\t\t\t\tair\n\t\t\t\t\t.
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One example for 20 July 2007 in Ljubljana is presented in Fig. 3. Based on these data the module efficiency was computed and is presented in Fig. 3c. Due to the higher reflection from the module by large incident angles, the efficiencies in early morning and late afternoon hours are quite low. Instead of being some 11 or 12% (as the module’s temperature at that time is low!) the calculated values are even below 9%. Between 8:30 and 12:30, when solar rays are more perpendicular to the module (low reflection), the module
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Figure 3.
a) Measured tilted irradiance E\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ttilt\n\t\t\t\t\t\t\t in the plane of the PV module (τ=30º, α=180º) oriented to the South on a clear day on 20 July 2007 in Ljubljana – with the Sun being occulted by a cloud at 15:20; b) measured power P\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tPV\n\t\t\t\t\t\t\t obtained of a typical polycrystalline module (S=1.634 m2) with the same tilt and orientation; c) measured efficiency η\n\t\t\t\t\t\t\t= P\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tPV\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t/S/E\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ttilt\n\t\t\t\t\t\t\t (η\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tSTC\n\t\t\t\t\t\t\t = 12.3%); and d) temperature of module T and of the surrounding air on roof T\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tair\n\t\t\t\t\t\t\t being higher than the one measured at the met station (Topič et al., 2007).
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temperature increases from 45º C to 71º C and the η drops from 11.3% to 10.0%. The empirically estimated relative efficiency temperature coefficient is - 0.0044/K, which is close to the producer’s specification of the temperature coefficient of the maximal output power γ = - 0.004/K.
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3. Case study
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The case study area presented in this chapter is Slovenia – a country on the south-east flank of the Alps between the Mediterranean and the Pannonian plain (approximately 13.5°-16.5°E and 45.5°-47.0°N). The country’s great topographical variety significantly influences the climate characteristics, which results in annual solar radiation variations and influences the orientation of PV modules.
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3.1. Data
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The majority of pyranometers installed at meteorological stations in Slovenia have been functioning since 1993 or even later. The study was therefore done on just 10-year-long data sets (Kastelec et al., 2007) and not on a 30-year period, which is the climatologically established standard. Global solar irradiation was during 1994–2003 measured at 12 meteorological stations (on average, one per approximately 2,000 km2). Air temperature measurements were also taken from the same meteorological stations.
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Map of ten-year average of annual global solar irradiation exposure was done by spatial interpolation of measured data on 12 locations and estimated data of global irradiation exposure on the basis of measured sunshine duration on 15 additional locations using Ångström’s formula (Fig. 4).
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Annual global radiance exposure changes significantly due to the country’s great climatic variety even over short distances. No data across the Slovenian border was taken into account by spatial interpolation, so the accuracy of interpolated values is lower in the regions near the borders especially in the mountainous western and southern parts.
\n\t\t\t\t
The diffuse part of the incoming solar energy was determined statistically by the Meteonorm 5.0 model package (Meteotest, 2003) at the remaining stations. The diffuse part of the incoming energy contributes a relatively smaller proportion to the global radiance exposure during summer (approximately 35–45%), and a relatively greater one during winter when there is even more diffuse than direct radiance exposure (up to 60%).
\n\t\t\t\t
Figure 4.
Interpolated average annual global solar irradiation exposure has a heterogeneous spatial distribution in Slovenia (average for the 1994–2003 period; Kastelec et al., 2007).
\n\t\t\t\t
The surface albedo was estimated by satellites. MODIS MOD43B3 albedo product (NASA, 2010) was used in the study, more specifically the shortwave (0.3–5.0µm) white sky broadband albedo. The MOD43B3 albedo product is prepared every 16 days in a one-kilometre spatial resolution. A reprocessed (V004) MOD43B3 albedo product is available from March 2000 till the present (thus not for the same time interval as used for global radiance exposure). Fig. 5 shows the annually averaged albedo over Slovenia for the 2000–2007 period.
\n\t\t\t\t
Figure 5.
Yearly averaged albedo (2000–2007) of the surface in Slovenia using MODIS images in a 1,000 m spatial resolution. Locations of four locations whose results are shown in the case study are also marked.
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
3.2. Computational simulation
\n\t\t\t\t
We computed the energy output for each combination of a tilt and azimuth angle for all months and for the whole year. This gives us the optimum combination of both geometry parameters for each period. In the same way we get also the increase or decrease of the energy received on any orientation of a PV in the chosen period. Our results are the graphs showing this increase/decrease relative to tilt τ and azimuth angle α are the most important results of this study. We ran the simulation using the IDL language. It took several minutes for each computation using a relatively powerful personal computer.
\n\t\t\t\t
Solar irradiance changes continuously over time in nature. Therefore, we decided to average the hourly measurements for 10-day periods. This resulted into 16-hourly averaged values (sunrise always after 4:00 and sunset always before 20:00) for each of the 36 periods. As meteorological measurements are performed at observing times according to UTC or to zonal time (CET) and not according to the true solar time, the distribution of the solar irradiance over the day is not symmetrical regarding the zonal noon. This can lead to errors of 20° by estimation of the optimal azimuth angle in March. The hourly data were thus fitted to a 5th order polynomial and then the irradiance and temperature values were estimated for each one hundredth of an hour. These values (at the end 16,000 for each of the 36 periods) were used in the simulation.
\n\t\t\t\t
The MOD43B3 albedo product was averaged for the 2000–2007 period (this product was not available for earlier years) over each month. Then it was projected to the Slovenian national co-ordinate system into a regular grid of a 1,000 m spatial resolution. Due to cloud coverage, some albedo datasets contain data gaps; these were in our case study removed during temporal averaging.
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
4. Results
\n\t\t\t
The results are presented for four locations in Slovenia (see their locations in Fig. 5). The graphs (Figs. 6–9) and Table 1 present the relative gain of energy (as a percentage) for the optimal combination of the inclination and orientation (marked by a cross) in comparison to energy on the horizontal surface. The abscise axes correspond to the azimuthal orientation (clockwise from the North) for azimuths from E to W (90° to 270°) and ordinate axes to the tilt (zero when the surface is horizontal and 90° for a vertical receiving surface). There are some differences among the four places, along with some common attributes. It is important to stress that optimal orientations and tilts are strongly affected by local weather and climatic conditions.
\n\t\t\t
Figure 6.
Contour plots of the relative PV array energy yield regarding the horizontal surface as a function of a fixed orientation and tilt for March, June, September and December as well as the whole year for Portorož in the Mediterranean part of Slovenia.
\n\t\t\t
Figure 7.
As for Figure 6, but for Ljubljana in a basin in central Slovenia.
\n\t\t\t
Figure 8.
As for Figure 6, but for Kredarica in high mountains.
\n\t\t\t
Figure 9.
As for Figure 6, but for Murska Sobota in the Pannonian part of Slovenia
\n\t\t\t
\n\t\t\t\tFigures 6–9 and Table 1 show that the PV modules should be oriented more or less towards the South – but not exactly; in Portorož and Ljubljana the optimal orientation is around 5° from the South towards the West. The main reason for this is that the effect of morning fog or low cloudiness, making the irradiance asymmetrical around (true) noon, prevails over the effect of lower efficiency in early afternoon hours due to the higher temperature of the module. The situation at Kredarica in this respect is very specific due to the mountain wall of the top cone of Mt. Triglav to the West of the location. Since there is a lot of shadow in the afternoon, the modules should be considerably oriented towards SE (α=155º). In the Pannonian part of Slovenia, in the warm part of the year a considerable proportion of precipitation is caused by convective cloudiness – and the fact that convective clouds normally develop in the early afternoon is also reflected in radiance exposures in Murska Sobota – especially in June and September the orientation from the South more to the East is clearly expressed. Thus not only monthly but even the optimal fixed annual orientation and tilt perform slightly better than using “a rule of thumb”, especially in places with a complex horizon (like at the mountainous Kredarica).
\n\t\t\t
The tilt angles are more season dependent as azimuth angles. For example, in December the optimal orientation for clear sky conditions should be South (180°) and considering only direct irradiation the tilt should be from 67º to 70º (depending on the latitude). However, as there is often fog and low cloudiness on winter mornings, the tilt may change considerably. For example in Ljubljana located in a basin (where such phenomena are most frequent) the optimal tilt is only 62º and the orientation 183º. In contrast, in June it is best to have the module more or less horizontal. The reason for that (at first glance quite unexpected result) is the high solar elevation; in June the Sun rises north from East (at approximately ENE in Slovenia) and also sets north from West (at approximately WNW in Slovenia). So a PV module might be in the shadow (no direct insolation) during early morning hours and late in the afternoon. Further, a tilted surface also receives less diffuse irradiance.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
Global radiance exposures (kWh/m2)
\n\t\t\t\t\t\t
Optimal orientation (º)
\n\t\t\t\t\t\t
Tilt for maximum Edir\n\t\t\t\t\t\t\tat solar noon (º)*
\n\t\t\t\t\t\t
Optimal tilt (º)
\n\t\t\t\t\t\t
Radiance exposures by optimal orientation and tilt (kWh/m2)
\n\t\t\t\t\t\t
Increase by optimal tilt and orientation according to global radiance exposures (%)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tPortorož on the Adriatic coast, φ = 45° 28´, λ = 13° 37´ h = 2 m a.s.l.\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
March
\n\t\t\t\t\t\t
110.2
\n\t\t\t\t\t\t
184
\n\t\t\t\t\t\t
45.5
\n\t\t\t\t\t\t
38
\n\t\t\t\t\t\t
133.0
\n\t\t\t\t\t\t
20.7
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
June
\n\t\t\t\t\t\t
202.2
\n\t\t\t\t\t\t
190
\n\t\t\t\t\t\t
22
\n\t\t\t\t\t\t
9
\n\t\t\t\t\t\t
204.1
\n\t\t\t\t\t\t
1.0
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Sept
\n\t\t\t\t\t\t
126.4
\n\t\t\t\t\t\t
185
\n\t\t\t\t\t\t
45.5
\n\t\t\t\t\t\t
34
\n\t\t\t\t\t\t
147.6
\n\t\t\t\t\t\t
16.8
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Dec
\n\t\t\t\t\t\t
33.6
\n\t\t\t\t\t\t
181
\n\t\t\t\t\t\t
67
\n\t\t\t\t\t\t
68
\n\t\t\t\t\t\t
68.4
\n\t\t\t\t\t\t
103.4
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
year
\n\t\t\t\t\t\t
1412.3
\n\t\t\t\t\t\t
184
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
29
\n\t\t\t\t\t\t
1573.1
\n\t\t\t\t\t\t
11.4
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tLjubljana in a basin in central Slovenia, φ = 46º 4´, λ = 14º 31´ h = 299 m a.s.l.\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
March
\n\t\t\t\t\t\t
97.4
\n\t\t\t\t\t\t
183
\n\t\t\t\t\t\t
46
\n\t\t\t\t\t\t
35
\n\t\t\t\t\t\t
113.8
\n\t\t\t\t\t\t
16.7
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
June
\n\t\t\t\t\t\t
178.5
\n\t\t\t\t\t\t
185
\n\t\t\t\t\t\t
22.5
\n\t\t\t\t\t\t
9
\n\t\t\t\t\t\t
180.4
\n\t\t\t\t\t\t
1.1
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Sept
\n\t\t\t\t\t\t
108.7
\n\t\t\t\t\t\t
190
\n\t\t\t\t\t\t
46
\n\t\t\t\t\t\t
32
\n\t\t\t\t\t\t
124.1
\n\t\t\t\t\t\t
14.1
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Dec
\n\t\t\t\t\t\t
23.8
\n\t\t\t\t\t\t
183
\n\t\t\t\t\t\t
69.5
\n\t\t\t\t\t\t
62
\n\t\t\t\t\t\t
38.2
\n\t\t\t\t\t\t
60.3
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
year
\n\t\t\t\t\t\t
1229.3
\n\t\t\t\t\t\t
185
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
25
\n\t\t\t\t\t\t
1329.3
\n\t\t\t\t\t\t
8.1
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tKredarica in high mountains, φ = 46º 23´, λ = 13º 51´ h = 2514 m a.s.l.\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
March
\n\t\t\t\t\t\t
121.3
\n\t\t\t\t\t\t
161
\n\t\t\t\t\t\t
46.5
\n\t\t\t\t\t\t
51
\n\t\t\t\t\t\t
157.9
\n\t\t\t\t\t\t
30.2
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
June
\n\t\t\t\t\t\t
155.9
\n\t\t\t\t\t\t
110
\n\t\t\t\t\t\t
23
\n\t\t\t\t\t\t
16
\n\t\t\t\t\t\t
160.6
\n\t\t\t\t\t\t
3.0
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Sept
\n\t\t\t\t\t\t
107.7
\n\t\t\t\t\t\t
147
\n\t\t\t\t\t\t
46.5
\n\t\t\t\t\t\t
40
\n\t\t\t\t\t\t
129.5
\n\t\t\t\t\t\t
20.2
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Dec
\n\t\t\t\t\t\t
44.3
\n\t\t\t\t\t\t
172
\n\t\t\t\t\t\t
70
\n\t\t\t\t\t\t
75
\n\t\t\t\t\t\t
108.7
\n\t\t\t\t\t\t
145.3
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
year
\n\t\t\t\t\t\t
1282.5
\n\t\t\t\t\t\t
154
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
42
\n\t\t\t\t\t\t
1538.5
\n\t\t\t\t\t\t
20.0
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tMurska Sobota on Pannonian flatlands, φ = 46º 39´, λ = 16º 11´ h = 188 m a.s.l.\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
March
\n\t\t\t\t\t\t
99.7
\n\t\t\t\t\t\t
179
\n\t\t\t\t\t\t
46.5
\n\t\t\t\t\t\t
34
\n\t\t\t\t\t\t
115.1
\n\t\t\t\t\t\t
15.4
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
June
\n\t\t\t\t\t\t
184.9
\n\t\t\t\t\t\t
170
\n\t\t\t\t\t\t
23
\n\t\t\t\t\t\t
9
\n\t\t\t\t\t\t
186.9
\n\t\t\t\t\t\t
1.1
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Sept
\n\t\t\t\t\t\t
109.8
\n\t\t\t\t\t\t
185
\n\t\t\t\t\t\t
46.5
\n\t\t\t\t\t\t
31
\n\t\t\t\t\t\t
124.1
\n\t\t\t\t\t\t
13.0
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Dec
\n\t\t\t\t\t\t
26.8
\n\t\t\t\t\t\t
177
\n\t\t\t\t\t\t
70
\n\t\t\t\t\t\t
68
\n\t\t\t\t\t\t
47.1
\n\t\t\t\t\t\t
75.8
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
year
\n\t\t\t\t\t\t
1275.3
\n\t\t\t\t\t\t
179
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
27
\n\t\t\t\t\t\t
1390.0
\n\t\t\t\t\t\t
9.0
\n\t\t\t\t\t
\n\t\t\t\t
Table 1.
Tilts for maximum E\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tdir\n\t\t\t\t\t\t at solar noon are rounded to 0.5 of a degreeOptimal azimuths and tilts according to months and the whole year and the resulting solar radiance exposures. The orientation for maximum E\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tdir\n\t\t\t\t\t\t at solar noon is 180° for all cases.
\n\t\t\t
It is also interesting that taking the temperature dependence of the PV module on efficiency into account does not greatly influence the optimal orientation and tilt. A comparison with optima for the solar radiance exposures alone, i.e. the isolation of natural surfaces (Rakovec & Zakšek, 2008), only shows here and there some differences in optimal orientations and tilts. Most of the results are equal (within a degree or two). The main reason for this is evident in Figure 3 where one can notice that although the efficiencies are not exactly symmetrical around noon – they are slightly smaller in the afternoon than in the morning hours – the asymmetry does not influence the optimal orientation essentially – by more than a degree or so.
\n\t\t\t
The albedo of the surrounding landscape influences the gain mainly at greater tilts of the modules when they “see” a considerable proportion of the ground in their half space; with tilts of around 70º the proportion is roughly 40% ground and 60% sky. As high tilts are favourable in winter, and as it is possible that there is snow cover in winter, with a high albedo, the ground may be even brighter than the sky. Such details are not included in our “monthly average” albedo – except for mountainous locations where snow in winter is regular and hence captured by satellite data.
\n\t\t\t
A comparison with some other studies for Slovenia, e.g. PVGIS (Huld et al., 2008) using a yearly averaged albedo and isotropic model proposed by (Liu & Jordan, 1963), shows that the optimal yearly tilts are significantly larger than in our study (PVGIS 35º for almost the whole of Slovenia versus ours e.g. 25º in Ljubljana; Table 1). If in addition the surface albedo is also overestimated (most models use 0.2, while the average yearly albedo equals e.g. 0.14 in Ljubljana) the results overestimate the actual gains by some 2–3%. The difference in gains could also be a consequence of an interpolation inaccuracy – PVGIS interpolated results for the whole of Europe and we estimated our results for chosen locations. The method considers the heterogeneity of the country by using solar irradiance characteristics that have different seasonal and daily courses in different parts of the country. These climatic differences accompanied by the albedo\'s heterogeneity therefore lead to different optimal azimuthal angles and tilts of the PV modules.
\n\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Location
\n\t\t\t\t\t\t
Hgl (kWh/m2)
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tmaxH* (kWh/m2)
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tHrt\n\t\t\t\t\t\t\t(kWh/m2)
\n\t\t\t\t\t\t
Hrt/maxH (%)
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\tHfix \n\t\t\t\t\t\t\t(kWh/m2)
\n\t\t\t\t\t\t
Hfix/maxH* (%)
\n\t\t\t\t\t\t
Wel (kWh/m2)
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Portorož
\n\t\t\t\t\t\t
1412.3
\n\t\t\t\t\t\t
1641.1
\n\t\t\t\t\t\t
1560.8
\n\t\t\t\t\t\t
95.1
\n\t\t\t\t\t\t
1573.1
\n\t\t\t\t\t\t
95.8
\n\t\t\t\t\t\t
160.2
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Ljubljana
\n\t\t\t\t\t\t
1229.3
\n\t\t\t\t\t\t
1367.0
\n\t\t\t\t\t\t
1311.6
\n\t\t\t\t\t\t
96.0
\n\t\t\t\t\t\t
1329.3
\n\t\t\t\t\t\t
97.2
\n\t\t\t\t\t\t
134.6
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Kredarica
\n\t\t\t\t\t\t
1282.5
\n\t\t\t\t\t\t
1655.7
\n\t\t\t\t\t\t
1498.5
\n\t\t\t\t\t\t
90.5
\n\t\t\t\t\t\t
1538.5
\n\t\t\t\t\t\t
92.9
\n\t\t\t\t\t\t
158.0
\n\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t\t\t\t
Murska Sobota
\n\t\t\t\t\t\t
1275.3
\n\t\t\t\t\t\t
1442.4
\n\t\t\t\t\t\t
1379.2
\n\t\t\t\t\t\t
95.6
\n\t\t\t\t\t\t
1390.0
\n\t\t\t\t\t\t
96.4
\n\t\t\t\t\t\t
141.0
\n\t\t\t\t\t
\n\t\t\t\t
Table 2.
maxH – Maximum solar radiance exposure is determined by considering monthly optimal orientations and tilts; such a maximum could even be increased by changing the orientation and tilt daily – but this is not a realistic option; among other reasons also due to the changing weather from day to day.Average annual solar radiance exposures; H\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tgl\n\t\t\t\t\t\t – solar global radiance exposure, maxH (see the note marked by *), H\n\t\t\t\t\t\t\n\t\t\t\t\t\t\trt\n\t\t\t\t\t\t – exposure by a fixed “rule of thumb” orientation 180º and tilt 35º, H\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tfix\n\t\t\t\t\t\t – by fixed optimal orientation and tilt, and W\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tel\n\t\t\t\t\t\t – electrical energy from a 215 Wp PV module with 85% system efficiency and with a fixed annual orientation and tilt at selected locations in Slovenia.
\n\t\t\t
On the basis of our simulations, it may be concluded that the best solution would be to change the orientation and inclination of PV modules during the course of the year (monthly, if technically possible; Table 1). But also for a fixed annual orientation and tilt the optimal orientation and tilt perform somewhat better than using “a rule of thumb”, especially in places with a complex horizon or specific climatic conditions – up to 3%.
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\n\t\t
\n\t\t\t
5. Conclusion
\n\t\t\t
To conclude, long-term measured meteorological values should be used to obtain reliable results on PV yield. Only then it is possible to dimension the PV system for yield optimization. We showed that the measured irradiation values are the most important parameter in photovoltaics. If only measurements of global irradiation are available, the diffuse part of irradiation can be simulated. Temperature measurements have merely a small effect on optimal orientation of PV system. Accurate albedo values are also irrelevant for the system orientation during the summer as albedo is usually low and optimal tilt angles are small. However in regions, where the albedo changes significantly during the year, is its accuracy important especially during winter, as the ground covered by snow is often even brighter than the sky.
\n\t\t
\n\t
Acknowledgments
\n\t\t\t
This work was funded by the Slovenian Research Agency under the P2/0197 programme and by the Slovenian Environmental Agency under contract 2523-04-300351. The Centre of Excellence for Space Sciences and Technologies SPACE-SI is an operation partly financed by the European Union, European Regional Development Fund and Republic of Slovenia, Ministry of Higher Education, Science and Technology.
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\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/17056.pdf",chapterXML:"https://mts.intechopen.com/source/xml/17056.xml",downloadPdfUrl:"/chapter/pdf-download/17056",previewPdfUrl:"/chapter/pdf-preview/17056",totalDownloads:9198,totalViews:290,totalCrossrefCites:6,totalDimensionsCites:10,hasAltmetrics:0,dateSubmitted:"October 27th 2010",dateReviewed:"April 6th 2011",datePrePublished:null,datePublished:"August 1st 2011",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/17056",risUrl:"/chapter/ris/17056",book:{slug:"energy-management-systems"},signatures:"Jože Rakovec, Klemen Zakšek, Kristijan Brecl,\nDamijana Kastelec and Marko Topic",authors:[{id:"31339",title:"Dr.",name:"Klemen",middleName:null,surname:"Zaksek",fullName:"Klemen Zaksek",slug:"klemen-zaksek",email:"klemen.zaksek@zmaw.de",position:null,institution:null},{id:"43754",title:"Dr.",name:"Joze",middleName:null,surname:"Rakovec",fullName:"Joze Rakovec",slug:"joze-rakovec",email:"joze.rakovec@fmf.uni-lj.si",position:null,institution:null},{id:"43755",title:"Dr.",name:"Kristijan",middleName:null,surname:"Brecl",fullName:"Kristijan Brecl",slug:"kristijan-brecl",email:"kristijan.brecl@fe.uni-lj.si",position:null,institution:null},{id:"43756",title:"Dr.",name:"Damijana",middleName:null,surname:"Kastelec",fullName:"Damijana Kastelec",slug:"damijana-kastelec",email:"Damijana.Kastelec@bf.uni-lj.si",position:null,institution:null},{id:"43757",title:"Dr.",name:"Marko",middleName:null,surname:"Topic",fullName:"Marko Topic",slug:"marko-topic",email:"marko.topic@fe.uni-lj.si",position:null,institution:null}],sections:[{id:"sec_1",title:"1. 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Available from https://lpdaac.usgs.gov/lpdaac/products/modis_products_table/albedo/16_day_l3_global_1km/mcd43b3\n\t\t\t'},{id:"B26",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tPetkovšek\n\t\t\t\t\t\t\tZ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRakovec\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1983 The influence of meteorological parameters on flat-plate solar energy collector. Archives for Meteorology, Geophysics, and Bioclimatology Series B, 33\n\t\t\t\t\t1-2 , 19\n\t\t\t\t\t30 , 0066-6424\n\t\t\t\t\n\t\t\t'},{id:"B27",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRakovec\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZakšek\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2008 Sončni obsevi različno nagnjenih in različno orientiranih površin (Solar radiance exposures of differently tilted and differently oriented surfaces). EGES, 12\n\t\t\t\t\t2\n\t\t\t\t\t93\n\t\t\t\t\t95\n\t\t\t\t\n\t\t\t'},{id:"B28",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tRakovec\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tZakšek\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t On the proper analytical expression for the sky-view factor and the diffuse irradiation of a slope for the isotropic sky. Submitted to Renewable energy, 0960-1481\n\t\t\t\t\t0960\n\t\t\t\t\t1481\n\t\t\t\t\n\t\t\t'},{id:"B29",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTian\n\t\t\t\t\t\t\tY. Q.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tDavies-Colley\n\t\t\t\t\t\t\tR. J.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tGong\n\t\t\t\t\t\t\tP.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tThorrold\n\t\t\t\t\t\t\tB. W.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001 Estimating solar radiation on slopes of arbitrary aspect. Agricultural and Forest Meteorology, 109\n\t\t\t\t\t1\n\t\t\t\t\t67\n\t\t\t\t\t74 , 0168-1923\n\t\t\t\t\n\t\t\t'},{id:"B30",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tTopič\n\t\t\t\t\t\t\tM.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBrecl\n\t\t\t\t\t\t\tK.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tSites\n\t\t\t\t\t\t\tJ.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2007 Effective efficiency of PV modules under field conditions. Progress in Photovoltaics: Research and Applications, 15\n\t\t\t\t\t1\n\t\t\t\t\t19\n\t\t\t\t\t26 , 0109-9159X\n\t\t\t'},{id:"B31",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tYakup\n\t\t\t\t\t\t\tM. A.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tbin\n\t\t\t\t\t\t\tH. M.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tMalik\n\t\t\t\t\t\t\tA. Q.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t2001 Optimum tilt angle and orientation for solar collector in Brunei Darussalam. Renewable Energy, 24\n\t\t\t\t\t2\n\t\t\t\t\t223\n\t\t\t\t\t234 , 0960-1481\n\t\t\t\t\n\t\t\t'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Jože Rakovec",address:"",affiliation:'
Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
Faculty of Electrical Engineering, University of Ljubljana, Slovenia
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Ragheb and Magdi Ragheb",authors:[{id:"32344",title:"Mr",name:"Adam",middleName:null,surname:"Ragheb",fullName:"Adam Ragheb",slug:"adam-ragheb"},{id:"33227",title:"Prof.",name:"Magdi",middleName:null,surname:"Ragheb",fullName:"Magdi Ragheb",slug:"magdi-ragheb"}]},{id:"16249",title:"Monitoring and Damage Detection in Structural Parts of Wind Turbines",slug:"monitoring-and-damage-detection-in-structural-parts-of-wind-turbines",signatures:"Andreas Friedmann, Dirk Mayer, Michael Koch and Thomas Siebel",authors:[{id:"43154",title:"Mr",name:"Andreas",middleName:null,surname:"Friedmann",fullName:"Andreas Friedmann",slug:"andreas-friedmann"},{id:"43159",title:"Dr.",name:"Dirk",middleName:null,surname:"Mayer",fullName:"Dirk Mayer",slug:"dirk-mayer"},{id:"43160",title:"Mr.",name:"Michael",middleName:null,surname:"Koch",fullName:"Michael Koch",slug:"michael-koch"},{id:"43161",title:"Mr",name:"Thomas",middleName:null,surname:"Siebel",fullName:"Thomas Siebel",slug:"thomas-siebel"}]},{id:"16250",title:"Magnetic Suspension and Self-pitch for Vertical-axis Wind Turbines",slug:"magnetic-suspension-and-self-pitch-for-vertical-axis-wind-turbines",signatures:"Liu Shuqin",authors:[{id:"48348",title:"Prof.",name:"Shuqin",middleName:null,surname:"Liu",fullName:"Shuqin Liu",slug:"shuqin-liu"}]},{id:"16251",title:"The Analysis and Modelling of a Self-excited Induction Generator Driven by a Variable Speed Wind Turbine",slug:"the-analysis-and-modelling-of-a-self-excited-induction-generator-driven-by-a-variable-speed-wind-tur",signatures:"Ofualagba, G and Ubeku, E.U",authors:[{id:"30605",title:"Dr.",name:"G",middleName:null,surname:"Ofualagba",fullName:"G Ofualagba",slug:"g-ofualagba"},{id:"43239",title:"Dr.",name:"E",middleName:null,surname:"Ubeku",fullName:"E Ubeku",slug:"e-ubeku"}]},{id:"16252",title:"Optimisation of the Association of Electric Generator and Static Converter for a Medium Power Wind Turbine",slug:"optimisation-of-the-association-of-electric-generator-and-static-converter-for-a-medium-power-wind-t",signatures:"Daniel Matt, Philippe Enrici, Florian Dumas and Julien Jac",authors:[{id:"28315",title:"Prof.",name:"Daniel",middleName:null,surname:"MATT",fullName:"Daniel MATT",slug:"daniel-matt"},{id:"44319",title:"Dr.",name:"Philippe",middleName:null,surname:"ENRICI",fullName:"Philippe ENRICI",slug:"philippe-enrici"},{id:"44320",title:"Dr.",name:"Julien",middleName:null,surname:"JAC",fullName:"Julien JAC",slug:"julien-jac"},{id:"86073",title:"Dr.",name:"Florian",middleName:null,surname:"Dumas",fullName:"Florian Dumas",slug:"florian-dumas"}]},{id:"16253",title:"Advanced Control of Wind Turbines",slug:"advanced-control-of-wind-turbines",signatures:"Abdellatif Khamlichi, Brahim Ayyat, Mohammed Bezzazi and Carlos Vivas",authors:[{id:"29938",title:"Prof.",name:"Khamlichi",middleName:null,surname:"Abdellatif",fullName:"Khamlichi Abdellatif",slug:"khamlichi-abdellatif"},{id:"29942",title:"Dr.",name:"Ayyat",middleName:null,surname:"Brahim",fullName:"Ayyat Brahim",slug:"ayyat-brahim"},{id:"29943",title:"Dr.",name:"Mohammed",middleName:null,surname:"Bezzazi",fullName:"Mohammed Bezzazi",slug:"mohammed-bezzazi"},{id:"29944",title:"Prof.",name:"Vivas Venegas",middleName:null,surname:"Carlos",fullName:"Vivas Venegas Carlos",slug:"vivas-venegas-carlos"}]},{id:"16254",title:"A Complete Control Scheme for Variable Speed Stall Regulated Wind Turbines",slug:"a-complete-control-scheme-for-variable-speed-stall-regulated-wind-turbines",signatures:"Dimitris Bourlis",authors:[{id:"28729",title:"Dr",name:"Dimitris",middleName:null,surname:"Bourlis",fullName:"Dimitris Bourlis",slug:"dimitris-bourlis"}]},{id:"16255",title:"MPPT Control Methods in Wind Energy Conversion Systems",slug:"mppt-control-methods-in-wind-energy-conversion-systems",signatures:"Jogendra Singh Thongam and Mohand Ouhrouche",authors:[{id:"44144",title:"Prof.",name:"Mohand",middleName:null,surname:"Ouhrouche",fullName:"Mohand Ouhrouche",slug:"mohand-ouhrouche"}]},{id:"16256",title:"Modelling and Environmental/Economic Power Dispatch of MicroGrid Using MultiObjective Genetic Algorithm Optimization",slug:"modelling-and-environmental-economic-power-dispatch-of-microgrid-using-multiobjective-genetic-algori",signatures:"Faisal A. Mohamed and Heikki N. Koivo",authors:[{id:"33855",title:"Dr.",name:"Mohamed",middleName:null,surname:"Faisal",fullName:"Mohamed Faisal",slug:"mohamed-faisal"},{id:"39905",title:"Prof.",name:"Heikki",middleName:null,surname:"Koivo",fullName:"Heikki Koivo",slug:"heikki-koivo"}]},{id:"16257",title:"Size Optimization of a Solar-wind Hybrid Energy System Using Two Simulation Based Optimization Techniques",slug:"size-optimization-of-a-solar-wind-hybrid-energy-system-using-two-simulation-based-optimization-techn",signatures:"Orhan Ekren and Banu Yetkin Ekren",authors:[{id:"30100",title:"Dr.",name:"Banu",middleName:null,surname:"Yetkin Ekren",fullName:"Banu Yetkin Ekren",slug:"banu-yetkin-ekren"},{id:"42011",title:"Dr.",name:"Orhan",middleName:null,surname:"Ekren",fullName:"Orhan Ekren",slug:"orhan-ekren"}]},{id:"16258",title:"Fuzzy Control of WT with DFIG for Integration into Micro-grids",slug:"fuzzy-control-of-wt-with-dfig-for-integration-into-micro-grids",signatures:"Christina N. Papadimitriou and Nicholas A. Vovos",authors:[{id:"29829",title:"Prof.",name:"Nicholas",middleName:null,surname:"Vovos",fullName:"Nicholas Vovos",slug:"nicholas-vovos"},{id:"29832",title:"Mrs.",name:"Christina",middleName:null,surname:"Papadimitriou",fullName:"Christina Papadimitriou",slug:"christina-papadimitriou"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"67013",title:"Real-Time Diffraction Field Calculation Methods for Computer-Generated Holograms",doi:"10.5772/intechopen.86136",slug:"real-time-diffraction-field-calculation-methods-for-computer-generated-holograms",body:'\n
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1. Introduction
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Holography is the only visualization technique that satisfies all the depth cues [1, 2, 3]. Therefore, it gives a natural three-dimensional (3D) visualization. Holography is based on capturing the diffracted optical waves from an object and regenerating those waves again by illuminating the recording media [1, 2, 3, 4, 5, 6]. Captured optical waves provide a significant amount of information related to the object such as surface profile, depth, and refractive index of the object. Hence, holography has a myriad of applications. For instance, holograms can be used as optical elements like prisms, lenses, and mirrors [7, 8]. Also, parallel optical computing is possible when holograms are employed [9, 10]. Furthermore, holograms are useful in metrology [11, 12, 13] and microscopic imaging to visualize very small objects like cells and bacterias [14, 15]. Another application of holography is related to nondestructive testing [16, 17, 18]. Nevertheless, major application of holography is related to 3D visualization, and it is used in education [19, 20], dentistry [21, 22], gaming [23], demonstration of cultural heritage [24], and more.
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Holography setups can be assembled by using different configurations depending on the application. In optical holography setups, holographic patterns are stored on high-resolution holographic films [25, 26] and some type of crystals [27]. However, in some of the applications, we need to process the captured holographic patterns by numerical methods. Then, digital sensing devices are employed as a capturing device. Those types of setups are called as digital holography, and it has a vast amount of applications especially in nondestructive testing and microscopy. In [28], digital holography-based measurement method of 3D displacement is presented. Observed material is illuminated from four different directions sequentially; then they are combined to improve the resolution in the order of 10 nm. As a nondestructive testing method, digital holography is used in the analysis of cortical bone quality and strength impact in [29]. Furthermore, a method based on digital holography is implemented for detecting and measuring effect of moisture on the hygroscopic shrinkage strain on wood [30]. Another application of digital holography is in precise and accurate measurement of the initial displacement of the canine and molar in human maxilla [31]. By using subpixel registration and fusion algorithms, an improvement of profile measurements and expanding the field of view (FOV) in continuous-wave terahertz reflective digital holography is achieved [32]. A comprehensive review of denoising methods on phase retrieval from digital holograms in terms of signal-to-noise ratio (SNR) and computation time is presented in [33]. Removal of phase distortions by using principal component analysis (PCA) method is given in [34].
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Holography is a versatile tool for visualization, measurement, and testing. In optical and digital holography methods, we need some optical sensing elements like polymers and digital devices to capture the diffracted field from the object. However, in computer-generated holography (CGH), diffraction field calculations are performed by using numerical methods and signal processing algorithms [4, 5, 6, 35]. Then, we can obtain the hologram from the calculated diffraction field and use it to drive dynamic display devices such as spatial light modulators (SLMs). After that, illumination of the SLM with a coherent light source will provide an optical reconstruction of the original object. When CGHs are calculated sequentially and used in driving SLMs, then we can have a holographic 3D television (H3DTV) as a product. An overview on holographic displays is presented in [36]. Generally, coherent light sources are used in H3DTV systems, and those light sources can generate speckle noise in the reconstructions. Low computational method for improving image quality and decreasing the speckle noise in CGH is proposed in [37]. Diffraction field calculations as in CGH are also used in other 3D display systems to improve the resolution of reconstructed objects. For instance, in integral imaging-based 3D display system, distortions on the elemental images are corrected by using holographic functional screen [38].
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In diffraction field calculation from a 3D object, we have to generate a synthetic 3D object. There are plenty of ways for generating a synthetic 3D object in a computer. For instance, we can form a 3D object by using a set of point light sources which are distributed over the space. Those types of objects are called as point cloud objects. To calculate the diffraction field from a point cloud object, we superpose the diffraction fields emitted by each point light source [35, 39, 40, 41, 42, 43, 44]. Another 3D object generation method is based on stitching small planar patches. As in the process of diffraction field calculation from point cloud objects, once again the diffracted fields from each patch are superposed to obtain the diffraction field of the object [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55]. The third method which can be used in the generation of synthetic 3D object is based on having multiple two-dimensional (2D) cross sections of the object along the longitudinal axis. Then, superposition of diffracted fields from those 2D cross sections will give the diffraction field of the 3D object [56, 57, 58, 59, 60]. A detailed summary on CGHs in terms of resolution, field of view, eye relief, and optical setups for different 3D object generation methods can be seen in [61, 62].
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CGHs of the objects should be calculated rapidly to obtain H3DTV systems. Hence, fast methods such as fast Fourier transform (FFT) and look-up table (LUT)-based methods are utilized in CGH calculations. In [39, 52], algorithms which are based on FFT are used for decreasing the calculation time of CGH. Precomputed LUTs are also used for achieving fast calculations in CGH calculations [2, 39, 41, 42, 63, 64]. Another way to achieve fast calculation in CGH is based on segmentation of diffraction field from point light sources [43, 44]. Parallel processing of diffraction field calculation provides further improvements on the computation time. Graphical processing units (GPUs) are special hardware to run parallel calculations. Thus, they are one of the most convenient hardware for H3DTV systems [40, 44, 65, 66]. Time-division method can also be used in the calculation of CGHs for layered 3D objects to achieve fast computations [67].
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Imposing some approximations in the diffraction field calculations provides to decrease the computational complexity, and it paves the way to obtain fast diffraction field calculations. In the meantime, we have to improve the quality of the reconstructed object. An accurate calculation method of diffraction field which is based on angular spectrum decomposition is explained in [68]. Furthermore, diffraction field calculation methods for SLMs with pixelated structure are presented in [69, 70, 71]. However, the computational complexities of those methods are too high to have real-time diffraction field calculations. As a result of this, the algorithms presented in [72, 73, 74, 75] are proposed as a solution to both computation time and quality in the reconstructed object in H3DTV. Further computational time improvements can be obtained by utilizing a LUT which is optimized for parallel processing on a GPU to achieve real-time calculations. Moreover, the pixel structure of the employed SLM in the reconstruction process is taken into account in forming LUT. Calculated LUT has one-dimensional (1D) kernels to decrease the allocated memory space.
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2. Calculation of diffraction pattern used in driving SLM with pixelated structure
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In CGH, it is possible to obtain 3D reconstructions of both synthetic and real objects. By employing dynamic display devices like SLMs in the reconstruction process, we can have H3DTV systems. To drive SLMs, we have to calculate diffraction fields from 3D objects by using numerical analysis methods and signal processing techniques. Calculation of diffraction field depends on the 3D object generation method. In this work, we assumed that 3D objects are represented as point clouds, because it is one of the simplest methods in 3D object generation. The diffraction field of the 3D object is calculated by superposing the diffraction fields emitted from the points that form the 3D object.
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Superposition on diffraction field calculation from a point cloud object over a planar surface can be expressed as
where \n\nψ\n\n\nr\n0\n\n\n\n and \n\nψ\n\n\nr\nl\n\n\n\n are the diffraction fields over SLM and diffraction field at \n\n\nl\nth\n\n\n sample point of the 3D object, respectively. Surface of SLM is represented by the position vector \n\n\nr\n0\n\n=\n\nx\ny\n0\n\n,\n\n and the sampling points of 3D object are shown by
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\n\n\n\nr\nl\n\n=\n\n\nx\nl\n\n\ny\nl\n\n\nz\nl\n\n\n\n. We assume that Fresnel approximation is valid and the term \n\n\nh\nF\n\n\nr\n\n\n denotes diffracted field on the SLM from a point light source expressed as
where \n\nr\n=\n\nx\ny\nz\n\n\n, \n\nk\n\n is the wave number, and \n\nλ\n\n is the wavelength of the light source used in illumination of the object.
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Scaled and superposed diffraction fields from point light sources provide the diffraction field of the 3D object, and its phase component is used for driving the SLM. Then, entire surface of the SLM is illuminated by a plane wave. After that, the reflected optical wave from the surface of the SLM generates an optical replica of the 3D object. Most of the off-the-shelf SLMs have square pixels with very high filling factors like \n\n93\n%\n\n [76]. Hence, the filling factor in the simulated SLM is approximated as \n\n100\n%\n\n. The pixel structure of the simulated SLM is illustrated in Figure 1.
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Figure 1.
An illustration of the pixel structure of the simulated SLM.
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Simulation of optical setup can be improved when the pixelated structure of the SLM is taken into consideration. For that purpose, we have to perform surface integration over each pixel area on the SLM. It is assumed that gray value over each pixel area has a constant value. The diffraction field over SLM can be found as
where \n\nn\n\n and \n\nm\n\n stand for indices of SLM along \n\nx\n\n- and \n\ny\n\n-axes, respectively. It is also possible to represent Eq. (3) by scaling and superposing 2D kernels \n\n\nK\n\n\nα\nl\n\n,\n2\nD\n\n\n\n,
where \n\nP\n\n\nr\nl\n\n\n=\n−\njψ\n\n\nr\nl\n\n\n\ne\n\njk\n\nz\nl\n\n\n\n\n and \n\n\nα\nl\n\n=\n\n1\n\n\nλ\n\nz\nl\n\n\n\n\n\n 2D kernel \n\n\nK\n\n\nα\nl\n\n,\n2\nD\n\n\n\n can be decomposed into 1D kernels as
where \n\n\nx\nl\n\n\n and \n\n\ny\nl\n\n\n refer to locations of \n\n\nl\nth\n\n\n point light source, used in generation of 3D object, along \n\nx\n\n- and \n\ny\n\n-axes, respectively. Each 1D kernel \n\n\nK\n\n\nα\nl\n\n,\n1\nD\n\n\n\n can be represented as
where \n\n\nζ\n\nl\n,\nn\n\n\n=\n\n\n\nx\nn\n\n−\n\nx\nl\n\n\n\n√\n\nλ\n\nz\nl\n\n\n\n\n\n. The operators \n\nC\n\n·\n\n\n and \n\nS\n\n·\n\n\n stand for cosine and sine Fresnel integrals, respectively [5, 6], and they are calculated as
Numerical evaluation of cosine and sine Fresnel integrals given in Eq. (8) is calculated by adaptive Lobatto quadrature [77].
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In the standard algorithm, diffraction field of each point is obtained by evaluating Eq. (8). Then, superposition of those fields is performed to obtain CGH. As a result of this, computational complexity of diffraction field calculation is too high to have real-time applications. As a solution to the computation time problem, we present a fast algorithm to calculate 2D kernel, \n\n\nK\n\n\nα\nl\n\n,\n2\nD\n\n\n\n, based on LUT and parallel processing.
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3. Proposed algorithm for fast calculation of CGH
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Fast computation of diffraction field and improved quality of reconstructed 3D object are essential issues in H3DTV. As a solution to those problems, we propose a method based on calculation of 2D kernels \n\n\nK\n\n\nα\nl\n\n,\n2\nD\n\n\n\n without evaluating sine and cosine Fresnel integrals. To achieve fast calculation, precomputed LUT is utilized, and the diffraction field of the 3D object can be obtained by scaling and superposing the 2D kernels \n\n\nK\n\n\nα\nl\n\n,\n2\nD\n\n\n\n as
where \n\n\n\nψ\n̂\n\n\n2\nD\n,\nz\n=\n0\n\n\n\n denotes the estimated diffraction field of the 3D object on the SLM and \n\n\n\nK\n̂\n\n\n\nα\nl\n\n,\n2\nD\n\n\n\n is the 2D kernel which denotes the diffraction field of \n\n\nl\nth\n\n\n point of the 3D object on SLM. 2D kernel \n\n\n\nK\n̂\n\n\n\nα\nl\n\n,\n2\nD\n\n\n\n is calculated by multiplying 1D kernels \n\n\nK\n\n\nα\nl\n\n,\n1\nD\n\n\n\n from LUT as shown in Eq. (5). Each 1D kernel \n\n\nK\n\n\nα\nl\n\n,\n1\nD\n\n\n\n represents the diffraction field on SLM from specific depth along longitudinal axis. A simple arithmetic operation is used for speeding up data fetching from the LUT. As result of this, total computation time of the diffraction field can be improved in terms of data fetching. By increasing the number of precomputed 1D kernels in LUT, we can achieve better diffraction field estimations for proposed method, but it causes to allocate more memory space. Hence, we apply different sampling policies along longitudinal axis to optimize memory space allocation. In the first sampling policy, uniform sampling along longitudinal axis is performed. In the second sampling policy, we sample the parameter \n\n\nα\nl\n\n=\n\n1\n\n\nλ\n\nz\nl\n\n\n\n\n\n uniformly. Thus, we have nonuniform sampling along the longitudinal axis.
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4. Simulation results
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Performance assessment of the proposed diffraction field calculation method is obtained by implementing different scenarios, but a few of them are presented to give an insight to the reader. Two major performance evaluation criteria are taken into account: total computation time of the CGH and the normalized mean square error (NMSE) on the reconstructed object. NMSE on the reconstructed object can be calculated as
where \n\n\nψ\n\n2\nD\n,\nz\n=\n\nz\n0\n\n\n\n\nn\nm\n\n\n and \n\n\n\nψ\n̂\n\n\n2\nD\n,\nz\n=\n\nz\n0\n\n\n\n\nn\nm\n\n\n denote reconstructed objects at \n\nz\n=\n\nz\n0\n\n\n plane from the diffraction field calculated by the standard and the proposed algorithms, respectively. Simulated scenario for a CGH is illustrated in Figure 2.
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Figure 2.
An illustration of simulated optical setup. The SLM employed in the setup has \n\nN\n\n and \n\nM\n\n pixels along \n\nx\n\n- and \n\ny\n\n-axes, respectively. Transversal axis sampling is indicated by \n\n\nX\ns\n\n\n. The variable \n\n\nz\n0\n\n\n determines the distance between SLM and the closest point light source of the 3D object.
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First, a 3D point cloud object is generated in computer environment. The generated 3D object has \n\n3144\n\n points which are distributed over the space. The volume occupied by the object has \n\n\nx\ne\n\n=\n2.8\nmm\n\n, \n\n\ny\ne\n\n=\n4.1\nmm\n\n, and \n\n\nz\ne\n\n=\n4.1\nmm\n\n extensions along \n\nx\n\n-, \n\ny\n\n-, and \n\nz\n\n-axes. There is a distance between the object and the screen, and it is taken as \n\n\nz\n0\n\n=\n61.6\nmm\n\n. We assume that simulated SLM has \n\n100\n%\n\n fill factor and pitch distance \n\n\nX\ns\n\n\n is taken as \n\n8\n\nμm\n\n. Also, the simulated SLM has \n\n512\n\n pixels along both \n\nx\n\n- and \n\ny\n\n-axes, respectively. We assume that green laser is employed for illumination purpose; hence the wavelength is taken as \n\n532\n\nnm\n\n.
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The proposed algorithm is implemented by using two platforms: MATLAB and Visual C++. To have shorter computation time for diffraction fields, we utilize CUDA libraries and parallel computation power of GPU. The assembled computer system has i5-2500 CPU at 3.3 GHz, 4GB RAM, and a GTX-680 GPU to run the algorithm. Operating system of the computer is chosen as 64-bit Windows 7.
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Generally, off-the-shelf SLMs have pixelated structure, and phase parts of the calculated diffraction fields are used for driving the SLM. When the pixelated structure of SLM is not taken into account in CGH calculations, it is not easy to differentiate focused and unfocused parts of the reconstructed 3D objects. An illustration of such a result can be seen in Figure 3a. As a result of the similarity in focused and unfocused parts, the quality of the reconstructed object is decreased significantly. On the contrary, the difference between focused and unfocused parts in the reconstructed 3D object is clear when the proposed method is used in diffraction field calculation. Those results can be seen easily in Figure 3b.
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Figure 3.
A point cloud object which has six parts and each part is located at different depths along the longitudinal axis. The leftmost piece is reconstructed in both of the figures shown above: (a) reconstruction of the 3D object from the CGH obtained without taking into consideration the pixelated structure of SLM and (b) reconstruction from the CGH calculated by the proposed algorithm.
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Furthermore, numerical and optical reconstructions are very similar to each other, and that similarity in the reconstructions can be seen in Figure 4.
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Figure 4.
(a) Optical reconstruction of a point cloud object and (b) numerical reconstruction of the same object given in (a).
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To calculate the diffraction field in the standard method, we need to perform cosine and sine Fresnel integrals for each pixel on SLM and for each point light source in 3D object. As a result of this, computational complexity of the standard method is extremely high, and CGH is calculated at \n\n2701.10\n\ns\n\n. Significant improvement in computation time can be achieved when the proposed algorithm is employed in CGH calculation. When we use LUT-based method for the same scenario which is mentioned above, we need \n\n8.15\n\ns\n\n to calculate the CGH. Further improvement in computation time can be obtained if the presented algorithm is implemented in parallel on a GPU. Although, significant gain on the computation time of CGH is obtained by using LUT, there will be negligible amount of error on the reconstructed objects, because of having finite number of kernels and the quantization effect along the longitudinal axis. The performance of the proposed method is summarized in Table 1.
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\n\n
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3D object = 3144 points; \n\nλ\n=\n532\n\nnm\n;\n\n N = M = 512; \n\n\nX\ns\n\n=\n8\n\nμm\n\n\n
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Computation time (s)
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NMSE
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\n\n\n
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Standard method
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2710.10
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—
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\n
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LUT
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8.15
\n
0.08
\n
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LUT: parallel processing by using four cores
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7.08
\n
0.08
\n
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LUT: parallel processing by using GTX-680
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0.08
\n
0.08
\n
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Table 1.
Performance assessment of the proposed algorithm in terms of NMSE.
Proposed algorithm utilizes LUT which has 1D precomputed kernels for 125 different sampling points along longitudinal axis.
\n
By increasing the number of kernels in LUT, we can improve error performance of the algorithm without having any extra computational load, but there is an increase in the size of the required memory. As a result of this, installed memory space may not be enough to perform the diffraction field calculations. To overcome memory allocation problem, we use another sampling policy in generation of LUT. Two different sampling policies along the longitudinal axis are proposed. The first sampling policy is based on uniform sampling of longitudinal axis. The second sampling policy is related to uniform sampling of \n\n\nα\nl\n\n\n. Hence, there will be nonuniform sampling along the longitudinal axis. Tables 2 and 3 summarize performances of the sampling policies in terms of NMSE and required memory allocation by the precomputed LUT. As it can be seen from Tables 2 and 3, when the size of the LUT is fixed, uniform sampling policy along longitudinal axis provides better NMSE performance than nonuniform one.
\n
\n
\n
\n
\n\n
\n
3D object = 3144 points; \n\nλ\n=\n532\n\nnm\n;\n\n N = M = 512; \n\n\nX\ns\n\n=\n8\n\nμm\n\n\n
\n
\n
\n
Number of 1D kernels
\n
NMSE
\n
Memory allocation (kB)
\n
\n\n\n
\n
83
\n
0.068
\n
332
\n
\n
\n
92
\n
0.061
\n
368
\n
\n
\n
103
\n
0.054
\n
412
\n
\n
\n
118
\n
0.048
\n
472
\n
\n
\n
137
\n
0.039
\n
548
\n
\n
\n
165
\n
0.034
\n
660
\n
\n
\n
206
\n
0.026
\n
824
\n
\n
\n
274
\n
0.020
\n
1096
\n
\n
\n
411
\n
0.014
\n
1644
\n
\n
\n
821
\n
0.006
\n
3284
\n
\n\n
Table 2.
Performance of the proposed algorithm according to the number of kernels used in LUT, NMSE, and allocated memory space.
LUT is formed by uniform sampling of depth parameter along longitudinal axis. Each element in 1D kernels is represented by four bytes.
\n
\n
\n
\n
\n\n
\n
3D object = 3144 points; \n\nλ\n=\n532\n\nnm\n;\n\n N = M = 512; \n\n\nX\ns\n\n=\n8\n\nμm\n\n\n
\n
\n
\n
Number of 1D kernels
\n
NMSE
\n
Memory allocation (kB)
\n
\n\n\n
\n
83
\n
0.127
\n
332
\n
\n
\n
92
\n
0.114
\n
368
\n
\n
\n
103
\n
0.104
\n
412
\n
\n
\n
118
\n
0.088
\n
472
\n
\n
\n
137
\n
0.077
\n
548
\n
\n
\n
165
\n
0.062
\n
660
\n
\n
\n
206
\n
0.051
\n
824
\n
\n
\n
274
\n
0.038
\n
1096
\n
\n
\n
411
\n
0.025
\n
1644
\n
\n
\n
821
\n
0.013
\n
3284
\n
\n\n
Table 3.
Performance of the proposed algorithm according to the number of kernels used in LUT, NMSE, and allocated memory space.
LUT is formed by uniform sampling of \n\n\nα\nl\n\n\n parameter. Each element in 1D kernels is represented by four bytes.
\n
In terms of calculated numerical errors, there should be a significant amount of deviation between reconstructed objects from CGHs obtained by standard and proposed method, but it is not easy to differentiate the reconstructions visually. Illustrations of numerically reconstructed objects by using both methods are shown in Figure 5a and b, respectively. To see the difference between to reconstructions, we subtract two reconstructions from each other and then take the magnitude of that difference. Then, we scale difference image linearly between 0 and 255 to improve the visibility of insignificant deviations. Those deviations can be seen in Figure 5c. Most of the deviations are in the unfocused region, and those deviations will not decrease the quality of the reconstruction. As a result of this, the proposed algorithm provides successful results.
\n
Figure 5.
(a) Magnitude of the reconstructed object at \n\nz\n=\n\nz\n0\n\n\n from the diffraction pattern calculated by standard algorithm and (b) by the proposed algorithm. (c) Magnitude of the difference between the reconstructed objects given in (a) and (b). Please note that image is scaled linearly from 0 to 255; thus the insignificant differences may become visible.
\n
Performance assessment of the presented algorithm is tested by optical reconstructions as well. For that purpose, we assembled an optical setup which is shown in Figure 6. Green laser with \n\nλ\n=\n532\n\nnm\n\n is used as a coherent light source, and HoloEye Pluto phase-only SLM is employed as a dynamic display device. A couple of optically reconstructed objects are shown in Figure 7.
\n
Figure 6.
Assembled optical setup for optical experiments.
\n
Figure 7.
Optically reconstructed 3D objects: (a) hand (b) propeller.
\n
\n
\n
5. Conclusions
\n
Two major problems in H3DTV systems can be called as decreasing the computation time of CGH and improving the quality of the reconstructed object. Using fast algorithms in diffraction field calculations will be helpful to decrease the computation time, but most of those fast algorithms impose some approximations that decrease the quality of the reconstructed object. In this work, we propose a diffraction field calculation algorithm that paves the way to achieve real-time calculations of diffraction fields from point cloud objects. In the meantime, the quality of the reconstructed objects is improved by taking into account the pixelated structure of SLM. Also, the proposed method can be run in parallel on a GPU. Performed numerical and optical experiments provide similar results. The proposed method utilizes precomputed LUT to decrease the computational load. To store the precomputed LUT, we need significant amount of memory allocation, and optimization of the occupied memory space is obtained by having two different sampling policies along the longitudinal axis. In the first sampling policy, LUT is formed by having uniform sampling along longitudinal axis. In the second one, nonuniform sampling is applied. When we fix size of the LUT, better NMSE performance is obtained by uniform sampling policy. As a result of this, when we use uniform sampling policy in computation of LUT, we need to allocate less amount of memory to store it.
\n
\n
Acknowledgments
\n
This work was supported by the Scientific and Technological Research Council of Turkey project under grant EEEAG-112E220 and Marmara University Scientific Research Fund project under grant FEN-A-130515-0176.
\n
\n',keywords:"computer-generated holograms, holographic display, real-time holography, spatial light modulators, 3D visualization",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/67013.pdf",chapterXML:"https://mts.intechopen.com/source/xml/67013.xml",downloadPdfUrl:"/chapter/pdf-download/67013",previewPdfUrl:"/chapter/pdf-preview/67013",totalDownloads:377,totalViews:0,totalCrossrefCites:0,dateSubmitted:"December 6th 2018",dateReviewed:"April 1st 2019",datePrePublished:"May 23rd 2019",datePublished:"September 25th 2019",dateFinished:null,readingETA:"0",abstract:"Holographic three-dimensional television systems provide a natural 3D visualization. Fast calculation of the diffraction field from a three-dimensional object is essential to achieve video rate. In the literature, there are myriads of fast algorithms for diffraction field calculation from three-dimensional objects, but most of them omit the pixelated structure of the dynamic display devices which are used in the reconstruction process. In this chapter, the look-up table-based fast algorithm for diffraction field calculation from a three-dimensional object for a pixelated dynamic display device is presented. Real-time diffraction field calculations are obtained by running the algorithm in parallel on a graphical processing unit. Performance of the algorithm is evaluated in terms of computation time of the diffraction field and the normalized mean square error on the reconstructed object. To have optimization on the required memory space for the look-up table, two different sampling policies along the longitudinal axis are implemented. Uniform sampling policy along the longitudinal axis provides better error performance than nonuniform sampling policy. Furthermore, optical experiments are performed, and it is observed that both numerical and optical reconstructions are similar to each other. Hence, the proposed method provides successful results.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/67013",risUrl:"/chapter/ris/67013",signatures:"Gokhan Bora Esmer",book:{id:"7682",title:"Holographic Materials and Applications",subtitle:null,fullTitle:"Holographic Materials and Applications",slug:"holographic-materials-and-applications",publishedDate:"September 25th 2019",bookSignature:"Manoj Kumar",coverURL:"https://cdn.intechopen.com/books/images_new/7682.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"191886",title:"Dr.",name:"Manoj",middleName:null,surname:"Kumar",slug:"manoj-kumar",fullName:"Manoj Kumar"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"288671",title:"Associate Prof.",name:"Gokhan Bora",middleName:null,surname:"Esmer",fullName:"Gokhan Bora Esmer",slug:"gokhan-bora-esmer",email:"gokhanbora@gmail.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Calculation of diffraction pattern used in driving SLM with pixelated structure",level:"1"},{id:"sec_3",title:"3. Proposed algorithm for fast calculation of CGH",level:"1"},{id:"sec_4",title:"4. Simulation results",level:"1"},{id:"sec_5",title:"5. Conclusions",level:"1"},{id:"sec_6",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Saxby G. Practical Holography. 3rd ed. Boca Raton, FL: Taylor and Francis; 2003. 478 p. ISBN: 978-1-4200-3366-3\n'},{id:"B2",body:'Lucente M. Diffraction-specific fringe computation for electro-holography [thesis]. Cambridge, MA: Massachusetts Institute of Technology; 1994\n'},{id:"B3",body:'Benton SA, Bove VM Jr. Holographic Imaging. New Jersey: John Wiley & Sons; 2008. 288 p. ISBN: 978-0470068069\n'},{id:"B4",body:'Toal V. Introduction to Holography. US: CRC Press Taylor and Francis Group; 2012. 502 p. ISBN: 978-1439818688\n'},{id:"B5",body:'Goodman JW. 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Applied Optics. 2008;47(19):3481-3493. DOI: 10.1364/AO.47.003481\n'},{id:"B71",body:'Katkovnik V, Migukin A, Astola J. Backward discrete wave field propagation modelling as an inverse problem: Toward reconstruction of wave field distributions. Applied Optics. 2009;48(18):3407-3423. DOI: 10.1364/AO.48.003407\n'},{id:"B72",body:'Esmer GB. Fast computation of Fresnel diffraction field of a three dimensional object for a pixelated optical device. Applied Optics. 2013;52(1):A18-A25. DOI: 10.1364/AO.52.000A18\n'},{id:"B73",body:'Esmer GB. Performance assessment of a fast and accurate scalar optical diffraction computation algorithm. 3D Research. IEEE; 2013;4(1):1-7. DOI: 10.1007/3DRes.01(2013)2\n'},{id:"B74",body:'Esmer GB. Algorithms for fast calculation of scalar optical diffraction field on a pixelated display device. In: IEEE AFRICON 2013; 9-12 September 2013; Mauritius: IEEE; 2013. DOI: 10.1109/AFRCON.2013.6757704\n'},{id:"B75",body:'Esmer GB. 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