Abstract: The application of an integrating sphere (IS) as a diffuser in a wireless ... As an example, a sphere diffuser for a 155 Mbit/s 16-PPM IR transmitter is.
OPTICAL WlRELESS COMMUNICATIONS
Integrating-sphere diffuser for wireless infrared communication V.Pohl, V.Jungnickel and C.von.Helmolt Abstract: The application of an integrating sphere (IS) as a diffuser in a wireless infrared (IR) network is investigated. Going beyond the simplified analytical model, it is shown that ray-tracing simulations provide realistic data for the optical insertion loss, the transfer function and the farfield light distribution. As an example, a sphere diffuser for a 155 Mbit/s 16-PPM IR transmitter is investigated with an insertion loss of 0.66 dB, a cutoff frequency of 570 MHz and a 104" full width at half-maximum (FWHM) angle of the intensity distribution. The device has also been manufactured using a proprietary material and good agreement between simulation and experimental data is found. A method to increase the FWHM angle and some aspects of eye safety are discussed.
Properties of integrating spheres
1 Introduction
2
Wireless IR networks are intended for indoors, especially when electromagnetic interference becomes an important issue [ l , 21. The IR light carrying the information is usually broadcast to the mobile users in the cell. However, most rooms are wider than they are high, and a transmitter having a wide radiation cone will be needed. In addition, it is easier to meet optical safety requirements when the transmitter area is large. A wide transmitter beam can be realised using a Lambertian diffuser. Its consine-law intensity distribution has a FWHM angle of 120". Diffuse reflections from rough surfaces often yield a nearly Lambertian distribution [3]. However, when the source is placed close to the diffuser surface, the source itself would shadow a sector in the cell. Recently, holographic diffusers have been proposed for wireless 1R systems [4]. However, their properties depend on the wavelength, and a hot spot in thc centre of the beam is present due to the undiffracted zero-order ray. The intensity in the hot spot can be controlled by careful hologram manufacture, but it is usually higher than the intensity in the diffused beam. The maximum optical safe power can thus be reduced. In this paper, the application of an IS as a diffuser is studied. The IS creates wider beams than common holographic diffusers, and it has nearly Lambertian intensity distribution basically independent from the IR-source characteristics. No hot spot is present, and a high optical power can be emitted to the room.
The ideal IS is a hollow spherical cavity with a diffusely reflecting internal surface. The total sphere surface is denoted as A,. The light is coupled into the sphere through a small entrance port with the area A ; . For the surface reflections, a Lambertian distribution with reflectivity p is assumed. Multiple diffuse reflections cause an almost constant radiance at the IS surface. For the application as a diffuser, part of this light is coupled out of the sphere through an exit port having the area A , . The fractional port area is then given by f = (A, AJA, . Frequently, the average reflectivity j = (1 - f l i p is used [5]. The optical insertion loss (IL) a and the cutoff frequency ,fo are defined in Section 11 (Appendix 1 1.1). It turns out, that an IS in the optical path of an IR transmission line is equivalent to a first order lowpass filter in the electrical path having the cutoff frequency ,fo. For modulation frequencies much larger than f o , the electrical power behind the photodiode will be reduced by 20dB per decade. Thus, the cutoff frequency of an IS diffuser must be matched to the desired data rate. Common 1% are relatively large (5-1 00 cm diameter). They are coated with highly reflective proprietary materials [6], and their fractional port area is smaller than 0.01 in order to maintain good Lambertian properties. The insertion loss and the cutoff frequency are investigated in Fig. 1 which are based on the formulas in Section 11.1. Clearly, the common ISs have rather large 1Ls. The 1L is smaller, however, when both the internal reflectivity and the fractional port area are large. The best values are obtained for spheres made using certain proprietary coatings and with fractional port areas up to 0.1. The best coating for this purpose [6] is a highly reflective synthetic diffuser material which can be processed using machine tools for large numbers of units. For example, an IL of 0.66dB is expected with ,f=0.06 and p = 0.99. Because the usual spheres are so large, they have a relatively low cutoff frequency. However, when the diameter is only 1 cm, a value o f f , = 570 MHz is expected.
0 IEE, 2000 IEE Proceediwgs online no. 20000564 DO[: 10.1049/ip-opt:20000564 Paper first received 29th September 1999 and in revised form 18th February 2000 The authors are with the Heinrich-Hertz-Institut fur Nachrichtentechnik Berlin GmbH, Einsteinufer 37, 10587, Berlin, Gertnany IEE h.oc.-O~itoelrctr-oii.,Vol. 147, No. 4, August 2000
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deviations are not described by the analytic sphere theory, a computer model by Ziegler et al. [8] is adopted here. In Fig. 2 the principle of the simulation model is shown. Starting from the entrance port (top), the random path of each photon is tracked. A random-number generator (see Section 11.2) is used to create a new direction as well as a decision whether the photon is reflected or absorbed at the reflection points on the inner surface. When the photon arrives at the exit port (bottom), the final direction of its flight and the total path length are noted. After a large number of trials, the insertion loss is then obtained by counting the fraction of photons leaving the sphere (When the Poisson distribution is used to describe the photoncounting process at the exit port [7], N = lo6 photons are for the required to estimate a relative error of l/JN= statistical data. Depending on the insertion loss the computation time for the C++ computer program is then about 15 min on a suitable personal computer having a clock speed of 266 MHz.). The angular intensity distribution is obtained by sorting the photons according to their final direction of flight. The impulse response comes from sorting the photons according to their time of flight. The transfer function is obtained by numerical Fourier transform of the impulse response. The simulation results forf, are taken at the -3 dB point in the frequency response. 4
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Fig. 1 Properties of conimon ISS a Optical insertion loss against reflectivity for various fractional port areas f b Cutoff frequency f, times sphere diameter as a function of the fractional port area for typical diffuser materials Curves obtained from eqns. 1-5 in Section 11.1 Filled circles refer to the sphere described in the text (i) Infragold (ii) DuraAect (iii) Spectralon
3 Ray-tracing simulations
Deviations from the Lambertian intensity distribution will to the relatively large port area. Since such
In the following, an IS with a diameter of 1 cm is studied. For the inner surface a Lambertian difhser with p = 0.99 is assumed. To obtain axial symmetry, the entrance and exit ports are placed opposite to each other, and a small target is fixed on the axis. After passing the entrance port, the first light ray falls onto the target where it is diffusely reflected (see Fig. 2). Fig. 3 displays the angular intensity distributions when the exit port area is increased. The Lambertian distribution is nearly obtained for f = 0.0 1. Insertion loss and cutoff frequency (a = 3.3 dB, fo= 145.6 MHz) are close to the analytical results (a = 3.1 dB, f o = 144.1 MHz), respectively. When f is increased from 0.01 to 0.06, the cone narrows slightly. The FWHM angle of the intensity distribution is reduced from 114" to 104", but a is reduced to
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statistics on 8 a n d time of flight Fig. 2 Principle ofthe ray-tracing simulation afier Ziegler et al [7] The random path of each photon is tracked; after a large number of trials statistical data for the diffuser are obtained 282
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Fig. 3 Intensity distribution for different port areas nornialised to the nzaximuni power (simulation results) ' __ Lambertian 0
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n ( t ) as is assumed in eqn. 4 in Section 1 I . 1 . Depending on the number of reflections, their time of flight is distributed statistically. When all these distributions are summed, the exponential decay, predicted by the analytical theory, is obtained when the width of h,(t) becomes comparable with
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Fig. 4 Impulse response of the axially symmetric sphere described in the text (simulation result) Labels h,(t) mark the separated temporal distributions of all photons leaving the sphere after n reflections Insert shows optical amplitude response obtained by numerical Fourier transform; lowpass behaviour according to theory is also plotted
Compared with the exponential decay, the relative amplitude of the initial peaks in Fig. 4 increases when 6 is reduced. Provided that 1 - f(8, 4)d+ d e = 3c
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