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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
1. Introduction
The optical invariant [1] instructs us that light having enhanced spatial coherence, as compared to natural sunlight, is necessary for useful delivery of optical power over the long distances encountered in space. Recent studies indicate that such light, as opposed to microwaves, e.g., is favored for useful delivery of power from space [2–5]. Optical amplification, or laser action, is a means, and probably the only practical means, of achieving the needed spatial coherence [3,5]. We describe safety standards for delivery using light produced by optical amplification, but configured to more closely resemble natural sunlight than the light typically produced by lasers.
1.1 Power available as natural sunlight in the vicinity of Earth
We can estimate the power available as natural sunlight in the vicinity of Earth. Consider the area of disk shaped region centered on Earth, but oriented normal to a line between the sun and Earth. Let the radius of this disk shaped region extend out to geostationary orbit, or ~36 megameters from Earth. The natural sunlight passing through this disk shaped region carries ~1018 watts of power. A small fraction of this clean renewable power is more than sufficient to satisfy the projected needs of Earth, and those of human exploration and development of space, far into the future [2].
Larger regions, e.g., out to the LaGrangian point, L1, nearly a gigameter from Earth can most likely be accessed in time. The Gaussian beam radius w at a distance L large compared to the Rayleigh distance for an initial beam radius wo given wavelength λ is ~Lλ/πwo. Thus an ~300 m beam radius at Earth only requires an emitting beam radius of 1 m in space. This current paper addresses key safety issues relevant to optical delivery of power from geostationary orbits in the vicinity of Earth. Other papers examine collection and amplification strategies [3,5].
1.2 Delivery of power from an array of uniformly distributed satellites
While our study indicates that that safe delivery of power to Earth is achievable, the upper limits on safe delivery change dramatically with optical wavelength. We provide explicit plots of the safety standards as a function of wavelength and examine the particular satellite constellations that satisfy the goal of safe power delivery.
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.
The satellite constellation, when viewed by an observer located at the receiving site on Earth and looking toward the constellation, appears as shown in Fig. 2. The safety criteria given in the following are developed for this, worst case, situation. An observer not at the receiving site will typically not see emission since the light is specifically delivered to the intended receiving site and only to that receiving site. Provided the criteria given in this current article are observed, this worst case and hence all other cases, are safe as defined by the referenced standards.
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.
While the observed pattern shown in Fig. 2 is simple, the satellites in the constellation are actually following a complex and specifically designed family of elliptical orbits. The combination of these orbits and the rotation of the Earth result in this, to the Earth based observer, apparently stationary constellation. Each successive ring of the family of concentric circles appears to the observer at Earth to retain its indicated shape and location; however, the individual satellites within a given circle follow a trajectory that carries them, in synchronism with the rotation of the Earth, around the circumference of the circle.
1.3 HALO orbits
The use of families of satellite orbits to achieve particular constellations as viewed by an observer at Earth has been a topic of interest for some time. The particular set of concentric orbits depicted in Figure 2 appears especially favorable for delivery of power from space and has been specifically explored by Penn, Chao, and others [6]. These orbits are referred to as HALO orbits, given the apparent circular trajectory of the satellites about a fixed point in the observer’s field of view. An analysis of the orbital mechanics indicates that subtended angles as large as 27° are viable from a stationkeeping point of view [6].
1.4 Prevention of violation of safety limits
A concern of some importance is that the optical technology on the satellites not allow unintended reconfiguration of the emission, as by remote control, in ways that might violate safety standards. The use of independent beams of differing wavelength and random relative phase, e.g., 10,000 beams per satellite, is helpful in this regard. This approach results in incoherent addition of multiple beams at Earth. By limiting the emission aperture of each beam to ~1 cm the illuminated area at Earth cannot be smaller than ~1km. By using different wavelengths and random phases for the set of beams the production of local intensity fluctuations at Earth significantly in excess of the mean intended intensity will not occur.
1.5 Advantages of safely delivered light enhanced in spatial coherence
Multiple advantages can be discerned for this light having enhanced spatial coherence and delivered from these distributed sources. Safety standards can be satisfied as well as, or better than, by natural sunlight. In addition the light has significant advantages over natural sunlight as regards delivery of power. The transmission is continuous and always arrives from the same general location in space. This corresponds to a gain of roughly a factor of 4 as compared to natural sunlight in integrated power delivered to a non-tracking receiver. The increased temporal coherence, as exhibited, e.g., in narrowed bandwidth, can yield increased solar cell conversion efficiencies by factors of 2 or 3 as compared to natural sunlight [8]. The potential for a seven-fold increase in intensity in the near infrared, while still satisfying safety standards, is also of interest. Strategies for working around weather conditions can be identified that use redirection of light among a family of spatially distributed sites at Earth.
2. Design Considerations for Satellite Constellation Geometry
In this section, we detail the procedure for determining the minimum number of satellites and the minimum dimensions of the constellation such that the resulting flux on Earth is both eye-safe and skin-safe. We begin by reviewing the existing safety standards. We express these standards as a function of the emission wavelength, the number of satellites, and the angular extent of the constellation.
The American National Standard for the Safe Use of Lasers [9], ANSI Z136.1-1993 provides a hazard classification scheme that describes the potential of a coherent optical beam or diffuse reflection of a coherent optical beam to cause biological damage to the skin or eye. This classification scheme applied in terms of lasers is: Class I lasers are considered incapable of producing biological damage, while Classes IIa, II, IIIa, IIIb and IV represent increasing levels of danger. This classification scheme is also contained in the U.S. Code of Federal Regulations [10]. The Class I laser limits are based on calculations of the Maximum Permissible Exposure (MPE) as set forth in ANSI Z136.1. The MPE for skin exposure and for eye exposure are calculated separately, and the Class I limit is the lower of the two MPEs.
Determining the MPE of a coherently emitting system requires knowledge of the wavelength(s) or wavelength range, the average power output and/or energy per output pulse, and the limiting exposure duration. Additionally, a coherently emitting system is considered an extended source if it consists of an array or if a permanent diffuser is incorporated into the output optics. In the case of an extended object, the viewing angle α subtended by the source must be considered.
2.1 Assumptions
In the following sections, we consider the wavelength range 0.4 µm≤λ<1.6 µm. Ultraviolet wavelengths (λ<0.4 µm) present acute risk to biological tissues and we therefore exclude them from consideration. Infrared wavelengths longer than 1.6 µm can be considered; however, the MPE calculations remain constant for all wavelengths in the range 1.4 µm≤λ<103 µm. Readers should note that all graphs in this report that end at 1.6 µm can be extended to 103 µm.
We presume a receiving site is identified and managed as such. Our analysis excludes special cases such as where an individual within the receiving area illuminated by the beam uses optical instruments, such as binoculars or telescopes, to look directly at the source. The eye safety MPEs need to be decreased if optical instruments are used in this manner. We do include the case where an individual at the receiving site looks with the unaided eye toward the satellites. This is thus a worst case approach since in most instances observers will not occupy a receiving site and the intensity off site (due to higher order components of the emission pattern) is expected to be orders of magnitude less than that on site.
We assume an illuminated region at the receiving installation that is at least 100 m2 and that has an essentially uniform irradiance distribution in any given square meter. This is reasonable given the 36×106 m distance from the satellite-based emitters to the receiving site, and the restricted emitting aperture [3,5]. The importance of this, locally uniform, distribution is the avoidance of local intensity peaks in the illuminated area. ANSI Z136.1 defines limiting apertures over which the irradiance must be integrated. For example, the limiting aperture for skin is typically 3.5 mm in diameter. Finally, we assume the emitting sources are continuous and not pulsed.
In keeping with the safety standards formulation we assume 3×104 s (approximately eight hours) for a skin exposure time. This allows continuous exposure for a typical workday. Safety standards define skin exposure MPE as constant from 3×104 s down to 10 s. For exposures shorter that 10 s, the skin safety limit increases.
We follow the guidelines in Section 8.2.2 of ANSI Z136.1 to determine the appropriate exposure times for use in the retinal MPE calculations. For visible wavelengths 0.4 µm to 0.7 µm, the retinal exposure duration is the human aversion response time of 0.25 s. This assumes purposeful staring into the beam is not intended nor anticipated. For the invisible, near IR, wavelengths 0.7 µm to 1.4 µm, a retinal exposure duration of 10 s is assumed. This should provide an adequate hazard criterion for either incidental viewing or purposeful staring. Natural eye motions make longer durations on an unseen object highly unlikely. Finally, for infrared wavelengths from 1.4 µm to 103 µm, the eye exposure duration is the same as the skin exposure (3×104 s). This follows in that the eye is opaque in this wavelength range [11].
2.2 Skin Exposure Limits
We begin our analysis by considering the MPE for skin exposure. We assume a maximum exposure time to be an eight-hour work day (~3×104 s), although the exposure limits remain the same for exposures as short as 10 s. From ANSI Z136.1, the skin exposure MPE for wavelengths from 0.4 µm to 1.4 µm is
where λ is given in µm and CA is a dimensionless correction factor given by
Figure 3 contains a plot of the resulting skin exposure MPE. For reference, 1.373 kW/m2 is the approximate solar irradiance at Earth’s surface [12]. For visible wavelengths, MPEskin is 2.0 kW/m2, or just less than 1.5 “Suns”. That value increases exponentially between 0.7 µm to 1.05 µm to a maximum MPEskin of 10 kW/m2. Note that this irradiance value is approximately seven Suns. At 1.4 µm, there is a discontinuity in the MPEskin calculation. Beyond 1.4 µm tissue becomes strongly absorbing. For beam diameters smaller than 100 cm2 and exposure times greater than 10 s, the MPE for skin exposure and the MPE for eye exposure are the same for wavelengths greater than 1.4 µm since the eye does not transmit in this region [11]. In all such cases the MPE is 1 kW/m2. However, as the beam becomes larger, the permissible irradiance actually decreases due to cumulative thermal effect arising from the strong absorption of that wavelength by tissue. For illuminated areas larger than 1000 cm2 (approximately one square foot), the MPE for skin irradiance reduces to 100 W/m2, as reflected in Eq. (1). Because exposed arms and face would likely exceed 1000 cm2, we set a maximum safe irradiance MPEskin of 100 W/m2 for wavelengths from 1.4 µm to 103 µm.
Note that the skin exposure limits do not consider the geometry of the source. It does not matter if the irradiance is generated from a single point-source or from an extended source. Of course, if optical elements are used to focus this light onto the skin, the optical invariant [1] indicates the image of a point source does more damage than the image of a large diffuse source. The refractive power of the cornea and crystalline lens of the eye present this same hazard consideration to the retina. As a simple example, viewing the filament of a 200-W incandescent bulb from several meters away can be quite uncomfortable, while viewing a 200-W bank of several fluorescent bulbs with diffuser screens is not. The MPE calculations for the eye consequently do consider the geometry of the source. For this reason, the skin exposure limits tend to be the dominant factor setting an upper limit on received intensity. As we will show in the following section, provided individual satellite-based emitters are distributed over some minimum angular dimension, the MPEskin can be achieved while also maintaining eye safety.
2.3 Eye Exposure Limits
ANSI Z136.1 provides separate MPE calculations for intrabeam viewing (i.e., direct observation) of point sources and for viewing of extended sources. The geometry of the proposed constellation of satellite-based lasers is explicitly considered by the ANSI standard. For non-uniform extended sources, each independent subsource of the extended object must first be considered a point source and the results compared with the corresponding MPE. Then, the entire ensemble of sources is considered as an extended source. Both the point-source and extended-source MPEs must be satisfied.
The retinal exposure MPE for a point source is calculated from
where t is the exposure time in s, λ is wavelength in µm, CA is the dimensionless correction factor from Eq. (2), and CC is another dimensionless correction factor given by
It is important to note that the retinal MPE calculations of Eq. (3) are valid for the exposure assumptions in Sec. 2.1, specifically, CW exposure times of t=0.25 s for 0.4 µm≤λ<0.7 µm, t=10 s for 0.7 µm≤λ<1.4 µm, and t=3×104 s for 1.4 µm≤λ<103 µm. Equation (3) remains valid for visible exposures as long as 10 s, and near IR exposures as long as 103 s. However, if the MPE calculations for longer exposures are required, the reader is referenced to Table 5 of ANSI Z136.1.
Figure 4 contains a plot of MPEpoint calculated from Eq. (3). Note that the irradiance values from Eq. (3) are measured at the cornea and do not represent retinal irradiance. While this seems counterintuitive, the ANSI standard chooses to present corneal irradiance values because, in practice, that is where the beam would be measured. The standard assumes a worst-case physiologic pupil diameter of 7.0 mm.
There are several discontinuities in slope and in value that occur in Fig. 4. These discontinuities serve primarily to provide needed simplification to the MPE calculations. The actual damage threshold of tissues varies more smoothly with wavelength. Figure 5 provides an illustration of the optical transmission of the human eye and the optical absorption of the human retina based on the data of Geeraets and Berry [13]. The absorption curve (solid line) indicates the fraction of light incident on the cornea absorbed by a typical human ocular fundus. This absorption characteristic drives the retinal MPE calculations in ANSI Z136.1.
Notice the sharp decrease in retinal absorption at 1.2 µm. This decreased absorption results in a marked increase in the retinal MPE as shown in Fig. 4. Also notice that the transmission of the eye quickly approaches zero at wavelengths greater than 1.4 µm due to the high absorption of tissues at these wavelengths. This increased tissue absorption is the reason for the dramatic decrease in the MPE described in Sec. 2.2. Additional discontinuities arise from changes in the assumed exposure time at 0.7 µm and 1.4 µm, as described in Sec. 2.1. Calculated MPE values in the immediate vicinity of these discontinuities have an approximate character.
The point-source exposure MPE required for eye safety limits the power that can be directed from a single satellite to a given receiving site. These values are significantly smaller than the skin exposure MPE (except for wavelengths greater than 1.4 µm where the limits are the same). Continuous extended sources in space over the required dimensions do not appear practical. The alternative examined here is that of using multiple discrete satellites arranged in a constellation that subtends a relatively large visual angle α. This creates a realizable “extended source” that offers improved eye safety and allows useful rates of power transfer.
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.
The extended-source MPE is calculated by multiplying the point-source MPE of Eq. (3) by a dimensionless correction factor CE
where α is the minimum visual angle subtended by the constellation, αmax=100 mrad, and
where t is the exposure duration in seconds (see Sec. 2.1).
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.
Given that no individual satellite-based source can contribute more than the point-source MPE of Fig. 4, we calculate the minimum number of satellites required to achieve the skin exposure MPE of Fig. 3. This minimum number of satellites is plotted verses wavelength in the top graph of Fig. 6. Finally, from CE we determine the minimum visual angle α that the constellation must subtend in order to meet the extended-source MPE limits. Minimum α values as a function of wavelength are plotted in the bottom graph in Fig. 6.
The optimum constellation geometry is one that, when viewed from Earth, is disk shaped and has individual satellites that are evenly spaced within the disk. For other geometries, one must consider that the smallest angular dimension of the constellation cannot be less than the angle α. Additionally, if the satellites are not evenly spaced, these calculations become much more involved due to the possibility of “hot spots” within the distribution. In this case, each possible sub-grouping of satellites needs to be considered independently. In general, without extraordinary special effort, the relative phase of the contributions from different satellites will be random and the contributions are to added incoherently.
2.4 One, Two, and Seven “Suns”
In Fig. 6, we illustrated the satellite constellation requirements for maximum permissible power transfer at each respective wavelength. In this section, we explore three particular irradiance values: the solar constant (S=1.373 kW/m2), twice the solar constant, and seven times S. Values up to seven Suns (9.6 kW/m2), satisfy the ANSI standard near 1 micron. Figure 7 illustrates the satellite constellation requirements for these three irradiance levels. In each case, values for the number of satellites and visual cone angle are plotted, but only for wavelengths at which the irradiance satisfies the safety standards (as per Fig. 3).
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.
3. Discussion and Conclusions
This study has demonstrated that an array of spatially coherent emitters in space can deliver up to seven times the natural solar irradiance on Earth and remain safe for human eyes and skin according to ANSI Z136.1. Consistent with the ANSI standard, we assume an eight-hour skin exposure, a ten-second infrared retinal exposure, and a 0.25 s visible retinal exposure. For infrared wavelengths between 1.05 µm and 1.4 µm, the upper limit of surface irradiance is 10 kW/m2. For wavelengths between 0.4 µm and 1.05 µm, the allowable irradiance levels are somewhat lower, as indicated in Fig. 3. The allowable surface irradiance decreases by two orders of magnitude (to 100 W/m2) for wavelengths longer than 1.4 µm if it is assumed that more than 1000 cm2 of skin are exposed.
For a space-based delivery system, a likely design goal is that of minimizing the required number of satellites. Fig. 7 provides guidance in this regard. The wavelength range that can safely deliver 9.6 kW/m2 (seven Suns) is 1.04 µm to 1.4 µm. Across this wavelength range, we find significant variability in the number of satellites required to meet eye safety limits. At wavelengths 1.05 µm≤λ<1.15 :m, 190 satellites are required, while at wavelengths 1.2 µm≤λ<1.4 µm, only 24 satellites are required. This represents a significant potential cost savings for a modest change of wavelength. Additionally, the visual angle α that the satellite constellation must subtend decreases from 26.2° to 9.3° between these wave bands. A smaller subtended angle results in simplified orbital mechanics for the proposed constellation, however even the 26.2° constellation appears realizable [6]. The 1.2 µm to 1.4 µm waveband appears optimal based on satellite constellation considerations. Sources may or may not be available at reasonable cost in this range. Future tradeoff studies will need to consider the relative merit of different wavelengths.
We have considered only the effects of direct illumination by coherent light. However, the eye safety of the diffusely illuminated ground, potential reflections from any buildings or structures, and light scattered by the atmosphere to off-site locations must also be considered. The diffusely illuminated ground and atmospheric scattering are not expected to present any risk since only Class IV lasers have been identified as capable of producing hazardous diffuse reflections. The design of a receiving site, and its potential for generating specular reflections (particularly focused reflections) will need to be integrated with a reflected light study. Also, we have neglected the effects of ambient sunlight. We expect that an otherwise safe 10 kW/m2 level would exceed skin safety limits when superimposed on an additional 1 kW/m2 solar irradiance. While it is tempting to assume that these irradiance values are simply additive, further study of this summation process appears warranted. Finally, as with any safety limit calculation, the MPE values presented in this paper represent the maximum permissible exposure and system designers should keep light levels well below these limits.
Much of this material was made available to participants in the recent NASA Space Solar Power Space Exploratory Research and Technology effort. The material in the graphs was available via the Marshall Space Flight Center Virtual Research Center starting in May of 2000. We thank J. Penn and C. Chao of Aerospace Corp. for discussions regarding the feasibility of using concentric arrays of HALO orbits to realize the angularly distributed satellite constellations discussed in this paper. Thanks are due Wesley W. Walker for verifying the calculations and a critical reading of the manuscript. Thanks are due Donna Fork for editorial assistance with the manuscript.
References and Links
1. See, e.g.D. O’Shea, Elements of modern optical design (John Wiley & Sons, New York, 1985).
2. J. C. Mankins, Testimony before the subcommittee on Space and Aeronautics, Committee on Science, House of Representatives, 9/7/2000. http://www.hq.nasa.gov/office/legaff/mankins9-7.html.
3. R. L. Fork, S. T. Cole, L. J. Gamble, W. M. Diffey, and A. S. Keys, “Optical amplifier for space applications,” Opt. Express 5, 292–301 (1999), http://www.opticsexpress.org/oearchive/source/14181.htm. [CrossRef] [PubMed]
4. Jerry Grey, Director of Aerospace and Science Policy, (AIAA), from the 9/7/2000House Science Committee’s Subcommittee on Space and Aeronautics hearing on Solar Power Satellites (SPS), http://www.nss.org/alerts/capsules/capsule50.html.
5. R. L. Fork, S. T. Cole, and W. W. Walker, manuscript in preparation.
6. J. P. Penn and C. C. Chao, personal communication. For an early reference on satellite constellations, see e.g., J.G. Walker, Jour. of the Brit. Interplanetary Society 35, .345–354 (1982).
7. S. T. Cole, M. H. Smith, and R. L. Fork, “Halo Satellite Orbit MPEG Movie,” http://www.uah.edu/LSEG/haloorbit. htm, (2001).
8. Carlos Algora and Vicente Diaz, “Design and Optimization of Very High Power Density Monochromatic GaAs Photovoltaic Cells,” IEEE Transactions on Electron Devices, 45, No. 9, Sept. p. 101, (1998). [CrossRef]
9. American national standard for the safe use of lasers, ANSI Z136.1-1993 (The Laser Institute of America, Orlando, FL, 1993).
10. Code of Federal Regulations, Title 21, Food and Drugs, Part 1040.10, Performance Standards for Light-Emitting Products, laser products (U.S. Government Printing Office, 1994).
11. D. Sliney and M. Wolbarsht, Safety with lasers and other optical sources (Plenum Press, New York, 1980).
12. CRC handbook of chemistry and physics, 79th edition, D. R. Lide, ed. (CRC Press, Boca Raton, FL, 1998).
13. W. J. Geeraets and E. R. Berry, “Ocular spectral characteristics as related to hazards from lasers and other light sources,” Am. J. Ophth. 66, 15–20 (1968). [PubMed]
