## 2 Design and Analysis of the Proposed Optical System
### Primary Analysis of the Designed Optical Module  
Figure 4 illustrates the overall shape and dimensions of the designed optical module, including its key components. As it is convenient to fabricate the CFL array plate and the lightguide separately, it is necessary to set an appropriate air-gap spacing distance, \(\Delta S\), for assembly. For this purpose, we examined the light power incident on the CCPC end surface according to the magnitude of \(\Delta S\). In this analysis, the transmittance and reflection due to the Fresnel loss were considered for both the CFL array plate and the lightguide. Figure 5 represents the transmitted power through the module and the concentrated power on the CCPC end surface according to the \(\Delta S\) values. When \(\Delta S\) was set to 1.3 mm, the concentrated light power on the CCPC end surface reached its maximum value of 1.475 W. At this point, considering the 5 W radiative power of the solar simulating light source, the transmittance through the optical module and the concentrated optical efficiency on the CCPC end surface were 54.1% and 29.5%, respectively.  
The designed optical module considers tracking the annual variation of the incidence angle of the sun, while not tracking the daily variation. In Figure 6, the angle notations for the rotation directions of the sun are defined. \(\alpha\) and \(\beta\) represent the incidence angle of the sun in the direction of daily variation and the incidence angle in the direction of annual variation, respectively, for the normal incident surface of the optical module. Thus, when both \(\alpha\) and \(\beta\) are \(0^{\circ}\), it is under DNI conditions. Considering tracking the annual variation of the incidence angle of the sun, when tracking without error, \(\beta\) is always \(0^{\circ}\). However, to examine the allowable tracking error, the transmittance and the concentrated  
Figure 4: Shape and dimensions of the designed transmissive light-concentrating optical module.  
Figure 3: Cross-sectional shape and parameters of the compound parabolic concentrator (CPC).  
light efficiency of the module were analyzed for \(\beta\) variations. Figure 7 illustrates the power transmitted through the module and the concentrated power on the CCPC end surface according to changes in \(\alpha\) and \(\beta\) when the incident solar power onto the CFL array plate is set to 5 W. In this simulation, we set the range of \(\alpha\) considering the range of \(\alpha\) where the amount of light transmitted to the CCPC end is more than 30% of its maximum value. As shown in Figure 7a, within the range of \(\mid\alpha\mid<15^{\circ}\) for the daily variation in the incidence angle of the sun, 28% of the incident solar power can be concentrated onto the CCPC end surface, and it can concentrate more than 16% up to \(\mid\alpha\mid<20^{\circ}\). At this point, the power transmitted through the module showed more than 50% transmittance within the range of \(\mid\alpha\mid<40^{\circ}\). As shown in Figure 7b, for the annual variation of the incidence angle, more than 28% of the incident solar power can be concentrated onto the CCPC end surface within the range of \(\mid\beta\mid<15^{\circ}\), and it can concentrate more than 15% within the range of \(1^{\circ}<\mid\beta\mid<20^{\circ}\). The reason for the sharp decrease in concentration efficiency onto the CCPC end surface for the annual variation in the incidence angle of the sun is due to the sun crossing the array direction of the CFL array, causing the incident angle onto the array axis to change.  
Figure 5: Transmitted power through the module and the concentrated power on the CCPC end surface according to the amount of \(\Delta S\).  
Figure 6: Definition of solar light incidence angle considering daily and annual sun path.