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Safe delivery of optical power from space

Matthew H. Smith, Richard L. Fork, and Spencer T. Cole

Open Access Open Access

Abstract

More than a billion gigawatts of sunlight pass through the area extending from Earth out to geostationary orbit. A small fraction of this clean renewable power appears more than adequate to satisfy the projected needs of Earth, and of human exploration and development of space far into the future. Recent studies suggest safe and efficient access to this power can be achieved within 10 to 40 years. Light, enhanced in spatial and temporal coherence, as compared to natural sunlight, offers a means, and probably the only practical means, of usefully transmitting this power to Earth. We describe safety standards for satellite constellations and Earth based sites designed, respectively, to transmit, and receive this power. The spectral properties, number of satellites, and angle subtended at Earth that are required for safe delivery are identified and discussed.

©2001 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Satellite constellation and Earth as seen from a viewpoint in space. The angle α, the distance from an observer (O) at Earth to the constellation, 36 Mm, and Earth are shown to scale. For illustrative purposes the satellites (white dots), are shown ~1000 times actual size. Inherent properties of the optics on the satellites, such as limited emission aperture, multiple beams of differing wavelengths and wavelengths and random relative phases can be used to ensure intensities at Earth based sites that remain within accepted safety standards.

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Fig. 2.
Fig. 2. Schematic showing a representative satellite constellation (white dots) as seen by an observer on Earth at the receiving site. For purposes of illustration the individual satellites are shown 1000 times actual size (as measured relative to the constellation diameter of ~17 Mm). The emission would typically not be observable to individuals not at the receiving site. The satellites populate concentric rings designed to produce a discretely, but on the average, uniformly populated area. Multiple interleaved constellations of this kind designed to deliver light to multiple spatially distinct sites are allowed by the orbital mechanics.

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Fig. 3.
Fig. 3. Maximum permissible exposure of skin to optical illumination.

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Fig. 4.
Fig. 4. Maximum permissible exposure of the eye to radiation from a single point-source.

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Fig. 5.
Fig. 5. Optical properties of the human eye. The dashed blue line indicates the intensity transmission from cornea to retina. The solid red line indicates fraction of the power incident on the cornea that is absorbed by the retina.

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Fig. 6.
Fig. 6. The top graph indicates the minimum number of satellite-based emitters required to achieve an irradiance equal to the skin exposure MPE from Fig. 3. The bottom graph indicates the minimum visual angle α required to meet safety standards.

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Fig. 7.
Fig. 7. Safety criteria for a satellite constellation delivering one Sun (dotted line), two Suns (dashed line), and seven Suns (solid line). One Sun is 1.373 kW/m2. These irradiance levels can be safely achieved only in certain wavelength ranges as indicated by the plotted curves.

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Equations (6)

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MPE skin = { 2.0 C A ; 0.400 ≤ λ < 1.400 0.1 ; 1.400 ≤ λ < 10 3 ( kW ⁄ m 2 )
C A = { 10 2 ( λ − 0.700 ) ; 0.700 ≤ λ < 1.050 5.0 ; 1.050 ≤ λ < 1.400 .
MPE point = { 0.018 t − 1 ⁄ 4 ; 0.400 ≤ λ < 0.700 0.018 C A t − 1 ⁄ 4 ; 0.700 ≤ λ < 1.050 0.090 C C t − 1 ⁄ 4 ; 1.050 ≤ λ < 1.400 1.0 ; 1.400 ≤ λ < 10 3 ( kW ⁄ m 2 )
C C = { 1.0 ; 1.050 ≤ λ < 1.150 10 18 ( λ − 1.150 ) ; 1.150 ≤ λ < 1.200 8.0 ; 1.200 ≤ λ < 1.400 .
C E = { 1.0 ; α < α min α ⁄ α min ; α min ≤ α < α max α 2 ⁄ ( α min α max ) ; α ≥ α max
α min = { 1.5 ; t ≤ 0.7 2 t 3 ⁄ 4 ; 0.7 < t < 10 11 ; t ≥ 10 ( mrad )
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