Hemispherical concentrators and spectral filters for planar sensors in diffuse radiation fields

Abstract

A dielectric hemisphere of refractive index N can act as an N(2) concentrator of isotropic diffuse radiation under appropriate conditions. We give an analytic expression for the gain of a concentrator of arbitrary radius, neglecting surface reflections, and numerical methods for calculating the gain when the surface transmissivity is an arbitrary function of incidence angle. The theory is applied to the design of multilayer spectral filters for hemispherical concentrators. When an appropriate wavelength shift is incorporated into the design process, an 11-layer, coupled-cavity spectral filter on the surface of a hemisphere of index 1.5 shows excellent bandpass performance with a concentrator radius as small as 3 times the sensor radius. This concentrator-filter combination shows a peak response of 97% of the ideal N(2) response at 950 nm, together with a FWHM of 55 nm.

Wireless Infrared Communications

“…The hemispherical lens is an important nonimaging concentrator [4], [16], [20], and is widely employed in commercial infrared systems [see Fig. 5(a) and (b)].…”

“…Instead, as shown in Fig. 5(b), the bandpass filter should be deposited or bonded onto the outer surface of the hemispherical concentrator [16], [20]. Regardless of the angle from which the signal is received, rays that reach the detector are incident upon the filter at small values of the angle , minimizing the shift of the filter passband, and maximizing its transmission.…”

“…6(b). One of the principal advantages of this link design is that, assuming that the transmitter illuminates a fairly small region of the ceiling, 16 the channel gain depends only on , the horizontal separation between the illuminated spot and the receiver, not the transmitter-receiver horizontal separation…”

“…A diffuse link need not employ a Lambertian transmitter, and the 15 As shown in [1], for very large incidence angles (of order 70 and larger), even nominally diffuse reflectors exhibit a strong specular component. 16 The diameter of the illuminated spot should be somewhat smaller than dsr. increase of path loss with can be made more gradual by employing several emitters angled in different directions [1], [32].…”

“…In infrared receivers, the total input capacitance is usually dominated by the detector capacitance , because of the large detector area required to achieve a high SNR. The total input-referred noise PSD of this preamplifier is (16) where the dominant contributions to the input-referred thermal noise PSD are given by (17) Here, is Boltzmann's constant, is absolute temperature, is the FET channel noise factor, and are the FET noise coefficients, and is the FET drain current. These PSD's are plotted in Fig.…”