## 3 Results
### Dosimetry for Therapeutic X-ray Beams
#### 3.2.4 Angular Dependence  
The normalized ratios for nine edgeless diodes to the TPS-predicted dose at 0\({}^{\circ}\) are presented in Figure 9. The selection of these diodes aims to emphasize the anticipated attenuation effects within the array structure with respect to the direction of the beam. Diodes located at a greater depth (specifically, D1, D3, and D5) exhibit a more pronounced angular dependency when compared with diodes positioned closer to the surface in respect to the beam direction (diodes D21, D23, and D25). Diode D21 demonstrates a consistent response, varying by no more than 3% across all irradiation angles, while diode D1 experiences a reduction in normalized dose ratio, reaching 4% for angles close to lateral irradiation (90\({}^{\circ}\)). The measurements for irradiation at an angle of 0\({}^{\circ}\) and 180\({}^{\circ}\) exhibited discrepancies of less than 1% for all diodes. Figure 8: The ratio of the responses of the central edgeless diode and IC is investigated with respect to DPP. The ratios are normalized to a DPP of 0.27 mGy/pulse, corresponding to SSD of 100 cm. The output of PP diodes was obtained using the edgeless array compared to the response of NN diodes. Figure 7: The output factor for the edgeless array detector is determined at a depth of 10 cm and SSD of 100 cm, and is normalized to the response under a 10 \(\times\) 10 cm\({}^{2}\) field. The responses of the CC04/CC13 IC and EBT3 Gafchromic Film [31] serve as benchmarks for evaluating the performance of the edgeless array. Error bars are contained within the symbols. The polar plots in Figure 10 illustrate the response of three diodes in comparison to the dose predicted by TPS at their respective positions, showcasing the normalized dose ratios with respect to the ratio obtained at a 0\({}^{\circ}\) irradiation angle. Figure 9: (**A**) The normalized dose ratios for edgeless diodes D1, D11, and D21 to the TPS-predicted dose at 0\({}^{\circ}\). (**B**) The normalized dose ratios for diodes D3, D13, and D23. (**C**) The normalized dose ratios for diodes D5, D15, and D25. Error bars represent the standard deviation based on three measurements with the edgeless array. Diode 20 exhibits high symmetry around 90\({}^{\circ}\) with a smoothly changing response function. In contrast, diode 4 displays a larger reduction response from 0\({}^{\circ}\) to 90\({}^{\circ}\) compared to the range between 90\({}^{\circ}\) and 180\({}^{\circ}\), accompanied by a discontinuous spike in the response at 90\({}^{\circ}\). Most diodes, including D19 in Figures 10 and 11, show a similar discontinuity, typically at or below 1%. Additionally, diode 19 demonstrates a slightly suppressed response between 90\({}^{\circ}\) and 180\({}^{\circ}\). All three diodes indicate an under-response of less than 1% when comparing face-up irradiation (0\({}^{\circ}\)) to face-down irradiation (180\({}^{\circ}\)). Furthermore, asymmetries in the response around 90\({}^{\circ}\) are consistently less than 1% for all diodes. In summary, although a maximum variation of 4% is observed with some pixels for angles between 80\({}^{\circ}\) and 120\({}^{\circ}\), the angular dependence of all diodes remained within 2% for irradiation angles below 80\({}^{\circ}\) and above 120\({}^{\circ}\). The array's angular dependence is visually represented in Figure 11 through a color map. Notably, the diode to TPS dose ratios in this case are not normalized to 0\({}^{\circ}\) but simply calculated as the ratio of the dose recorded by the sensor (calculated using the calibration factor described in Section 3.1) and the dose simulated by the TPS in the detector location. As the irradiation angle increases, the effects of attenuation from each silicon pixel become more evident, with dose ratios decreasing from approximately 1.02 to 0.97. The color map also highlights an increase in  
Figure 11: An overview of the study on angular dependence. The 2D color map illustrates the ratio of dose from the edgeless diode to the simulated TPS dose for each angle.