# Interference Filter Performance for Angles of Incidence Greater than Zero

In a TPV system, the radiation incident on a filter will arrive at all angles of incidence. Obviously, if the filter is designed for 9° = 0, then the optical performance at 0o > 0 will not be as good as at 0o = 0. Consider the embedded metal interference filter of Figure 4.9. For 0o = 45° the spectral performance of this filter for s polarization is shown in Figure 4.11.

 Figure 4.11a) – Transmittance, absorptance and reflectance for 0

of incidence, 0 =450. r ————– , P———- —– г а — — —

o

As Figure 4.11a shows, the center wavelength, Xc, moves to a shorter wavelength but the transmittance in the bandpass region is changed only slightly from the 0o = 0 case (Figure 4.9). In addition, the long wavelength performance at 0o = 0 and 0o = 45° is nearly the same. As 0o is increased beyond 45°, the degradation of performance is more pronounced.

This is illustrated in Figure 4.12 where the filter efficiency, %, is shown at a function of 0o for both s and p polarization. These calculations are performed using Xg = 1.9pm and TE = 1500K. In the case of p polarization, % actually increases for 0o > 80°. For s polarization, decreases rapidly for 0o > 50°.

 Figure 4.12 – Effect of angle of incidence, 0 on filter efficiency, ^ for the embedded metal interference filter of figure 4.9 at T =1500 K. Solid line p polarization, dashed line s polarization. Limit wavelength for filter efficiency calculation, X =1.9 um. g

Figure 4.12 shows that % = 0.5 for p polarization at 0o = 90°. It should be pointed out, however, that r ^ 0 and p ^ 1 as 0o ^ 90°. Therefore, even though remains finite, the amount of transmitted radiation is negligible.