Talk:Solar power satellite

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Contents

[edit] Tautology

"To be most cost effective, the system needs to operate at maximum capacity." This is a tautology, and though it is true, it is also necessarily true (being a tautology) thus providing no useful information. Sewercockroach 01:25, 13 October 2007 (UTC)

I don't understand your remark - diesel generators are more cost effective when run below maximum capacity because the wear increases non-linearly. --Jaded-view (talk) 20:07, 24 December 2007 (UTC)

[edit] misc early comments

Any reason this article isn't at solar power satellite, which to me seems like the appropriate name according to the naming conventions? --Robert Merkel

Newcomer ignorance. Mine. Rectified a bit since. user:mirwin

By the way, the article is overly optimistic about SPS's, and needs a little neutral point of view put into it by listing some of the critical views on the topic. --Robert Merkel

Perhaps. Some of what you seek is either at the bottom or solicited there. I put a reference to it at the top to encourage interested adherents of more pessimistic or alternate worldviews to seek them their.

Another Wikipedian started to wikify it but apparently got tired of it quickly. user:mirwin

[edit] Amortize space elevator costs?

Why does the cost of building a space elevator matter for the launch cost of solar satellites? Such an elevator would not be used only to launch this particular type of satellite, so the construction costs would be spread out over far more than this. Shouldn't only the estimated launch costs of $1-10/kg matter here?

We need to find investors for both the space elevator and the solar power satellite. Not even governments will invest if the cost is excessive. Without the space elevator, we must find a different cheap access to space. We don't know how many years we can realistically amortize either a space elevator nor the solar power satellite. In my opinion only the space elevator offers near term hope of $1 to $10 per kilogram launch cost. Perhaps we can live with $220 per kilogram. Ccpoodle 21:14, 3 July 2007 (UTC)

[edit] Focusing mirror better?

Wouldn't a satellite which directly focusses sunlight onto a solar thermal plant on earth be more efficient? The beam would be narrower than the microwave beam and the loss in thermal->electric conversion is less than that of solar cells. Clouds between the satellite and the ground station would quickly evaporate due to the intensive illumination. 193.171.121.30 02:12, 6 May 2005 (UTC)

It's not possible to use mirrors or lenses to focus the light from the sun more narrowly than the light from the sun already is. If you've ever fiddled around with a magnifying glass you should kinda know how this goes. You can make the image brighter though by collecting more light with a bigger lense. The microwave transmission technique actually gives a narrower beam, inspite of the wavelength being considerably longer. Sunlight-pumped lasers could also be used in principle; but in practice it's a weapon.WolfKeeper 02:19, 2005 May 6 (UTC)
Sorry, I don't quite understand you - you can focus sunlight from a larger mirror area onto a small spot on earth's surface where it can be used e.g. to evaporate and heat steam for a turbine which drives a generator to produce electric energy. A narrow beam is not necessary but a small spot at the earth's surface - and this spot can be made smaller at lower wavelengths with the same arperture size. I actually didn't mean narrow beam but small spot at the ground station. 193.171.121.30 12:45, 6 May 2005 (UTC)
Basically, what I'm saying is that it doesn't work. There are optical restrictions inherent in mirrors and/or lenses that prevent this from working. The angle that the light hitting the ground makes is the same as the angle that the sun makes at the satellite. This restricts how small the image it projects onto the ground can be. By making the mirror larger, you can make the image brighter, but not smaller. Because the satellite is so far away from the earth, the focused image is going to be very large. Something like that anyway... That's why the SPS was invented to circumvent this restriction. WolfKeeper
Thank you for the explanation - I should have given it a second thought before. 193.171.121.30 18:22, 6 May 2005 (UTC)

If the mirror is supported by a balloon about 1000 times closer the minimum spot size might be about the size of a typical solar site on the surface. We would not want the spot to be much brighter than the brightest sunlight, otherwise eye damage is likely.Ccpoodle 22:19, 22 May 2007 (UTC)

[edit] Cost feasiblity

Economic feasibility - don't we need to use the cost of power at the power stations, rather than the cost to consumers? (since the SPS power is still in one place and needs to be distributed) Ojw 12:54, 22 Jun 2005 (UTC)

Please explain the distinction that you're trying to make. Afterall, ignoring sunk costs, the SPS makes power for free. The real costs are in building it, managing it, and delivering the power to the grid. --Flatline 16:54, 2005 Jun 22 (UTC)
Distinction is: we are assuming that the SPS power station can sell electricity for the same cost that you pay at home. The calculation uses the $/kWh cost taken from the back of somebody's electricity bill, and not for the price that the power stations themselves are selling at.
If the two prices were equal, then there wouldn't be any money left over to buy power lines, transformers, fat-cat salaies, electricity meter-readers and everything else that the distribution company needs to get the electricity from an SPS antenna in the middle of a desert, to the consumers scattered around the nearest city.
This is different to (for example) solar-power roof tiles, where the power is generated at the consumer's home, so you can use the retail price of electricity to calculate how much it's saving you.
Ojw 18:28, 22 Jun 2005 (UTC)

I agree with Ojw The wholesale price is typically about half the retail price. The wholesale price will be very low during sunlight hours if there is lots of surface of Earth solar power. That is how supply and demand works.Ccpoodle 22:32, 22 May 2007 (UTC)

[edit] flexible power grid

an advantage of SPS is it can channel the power to receiving tower in different area as required. it is obvious to select places with high electric cost as the target market then move to cheaper/more competitive/more developed market.

[edit] Where did these values come from!

This sentance is likely erronous: To collect and convert that much power the satellite needs between 50 and 150 square kilometers of collector area thus leading to huge satellites.

Assuming a triple junction solar cell using mirror focusing a average efficiency of 25% is reasonable and within technological limits, with a solar constant of 1370 W/m2 the solar cells would produce 342.5W/m2, assuming a antenna and power conversions efficiency of 80% and a ground rectenna efficiency of 85% that would mean a total power production of 232.9W/m2, lets add in some more inefficiency leeway and round that off to 200W/m2. For a 4GW power station it would need 20,000,000m2 of solar panels or 20km2 or a square area of ~4.5km by ~4.5 km. Using cheaper single junction silicon polymer solar cell and focusing mirrors a max efficiency of 14% and total power production of 100W/m2 we would need 40km2 or 6.3km by 6.3km. --BerserkerBen 16:59, 24 July 2005 (UTC)

[edit] State of the art PV efficiency?

I haven't done the maths or anything like that, but isn't 40% or so the new 'state of the art' efficiency record? (http://www.energy.gov/news/4503.htm) The article should be updated if so. 203.166.229.35 12:40, 6 December 2006 (UTC)

40% may be the record, but such cells are not in mass production. State of the art for mass produced cells is presently 28.3% from Spectrolab, and possibly other suppliers.Charles 18:16, 6 February 2007 (UTC)

Efficiency is largely irrelevant here anyway per se. The most important metric is cost, and secondary to that is kW/kg (which translates into cost of launch). Only if the efficiency translates into lower weight is it important.WolfKeeper 18:41, 6 February 2007 (UTC)

342 watts per square meter is a reasonable near term goal, assuming the 50 square kilometers is kept pointed at the sun. Gathering the low voltage dc over an area of 50 square kilometers, will result in considerable wiring loss, even if the cells are in series parallel to produce ten million volts. A few of the million times a million cells will be shorted, open or marginal the first day and more will fail daily. Shorts and opens degrade other cells which are otherwise excellent. A means is needed to wire out (or replace) bad cells, if the photovoltaic array is going to continue in use for 40 years. 342 watts per square meter = 342 megawatts per square kilometer = 17.1 gigawatts of dc power for 50 square kilometers, so yes, the 150 square kilometers is pesimistic.Ccpoodle 23:10, 22 May 2007 (UTC)

[edit] Augment photovoltaics with mirrors?

There was recently some buzz about an idea called the Sunflower. This exploits the fact that mirrors and gears are cheaper than photovoltaics. A motor drives a 5x5 array of mirrors to track the sun, so the solar panel gets hit with 25 times as much sunlight as it would normally get. Presumably the same principle could apply to a solar power satellite. Use a big parabolic mirror made from metallized mylar, or whatever is the most practical and cost-effective material for space, and put the solar panel at the focus.


Yes, there have been designs for "solar dynamic" SPS and space power systems using parabolic mirrors, and Brayton cycle heat engines. The main disadvantage is that lots of moving parts has a reliability limitation, and potentially limited life. Repairing equipment in space is difficult, so long life of photovoltaics is a strong factor Charles 04:35, 3 February 2007 (UTC)

Photovoltaics have a limited life as well though, and are much more sensitive to radiation. Heat engines needn't be sensitive to radiation in any significant way. Also having moving parts does not necessarily imply limited life; for example hydrostatic or hydrodynamic bearings do not wear. I would imagine that the main lifetime limitations would be due to micrometeorite damage and/or loss of working fluids, but that should be pretty slow.WolfKeeper 04:57, 3 February 2007 (UTC)
Good points, I have added to the page a comparison of SD versus PV. Moving parts and bearings do have limited life; in space vacuum and temperature extremes mean the choice of lubrictants and working fluids is limited. Magnetic bearings are showing promise. Structures and mechanisms eventually suffer from metal fatigue, even composites can develop cracks. It is a question of design details such as stress levels and safety margins Charles 14:40, 3 February 2007 (UTC)

Perhaps solar wind could be used to keep it lined up with the sun, like the tail fins on a windmill. But then the original SPS idea must have involved some kind of active steering to keep the beam on the rectenna. Presumably the same mechanism could be used for aligning the mirror. WillWare 03:33, 27 August 2005 (UTC)

Solar wind is much weaker than photonic pressure; by a factor of 10 or more IRC. Still, you're right, it's easy to use photonic pressure for this. If the panels are laid out in a v-shape, the panel should self orient to point towards the Sun. There's no damping in space, so you'd also need some momentum wheels or something to damp out vibrations. The other trick is that the shape needs to be such that tidal forces don't make it tend to line up with the Earth, moon or Sun. I think if the shape is carefully chosen, it should be very stable. WolfKeeper

[edit] Other benefits of SPS

[edit] refs?

"Some research claims..." - Either give a reference or take the statement out. JonathanHart 11:57, 10 July 2006 (UTC)

[edit] PV lifetime?

Does anyone know how long solar cells can last in space? They have to endure hard radiation, particles from the sun and micrometeorites. By now there should be much practical experience from existing satellites. 84.160.212.221 19:31, 13 September 2005 (UTC) A small percentage of the satellites in GEO have operated for ten years, but there are failure reasons other than the solar panels. The 20 to 30 year estimates are likely based on likely future improvements, and may be over optimistic, especially for the multiple junction high efficiency types. On the surface of Earth, 20 year old photovoltaic panels typically produce about 1/2 their original output, so it appears they rarely die, but just fade away. My guess is 20 years is also optimistic for the magnetrons, klysitrons or solid state microwave producers. Ccpoodle 02:05, 15 June 2007 (UTC)

[edit] safety

Someone writes that the beam is relatively safe because if an aircraft were to fly through the beam, the passengers would be shielded by the effective Faraday cage. while that's true, I doubt the plane's electronics would be safe, as I'm pretty sure microwave beams were one method attempted with the Star Wars project. Isn't it enough that the FAA could regulate no-fly zones, as they do now? -jdw (user:71.196.216.187 on 1 Oct 2006)

If I recall correctly this question was part of the engineering evaluation done (mostly by NASA) in the decades after SPS was first proposed. The strength of the microwave broadcast carrying power to the Earth's surface was determined to be insufficient to affect birds (who do not have a metal Faraday cage surrounding them as do airline passengers). A sufficiently low power density of that beam implies a relatively large collecting antenna, and a workable design (cost effectiveness is a prime criterion in these designs) was found. So problems caused byt he beam are likely to be minimal unless the electronics involved are tuned to amplify the broadast signal.
As for the question about routing aircraft away from the beams is not necessary. The FAA currently does must this for flights over or near sensitive sites, such as military bases or high value terrorist targets such as public buildings, but each such arrangement further complicates airmans' references. They are already more complex than is really justfied. In short, it could be done but is not likely to be a satisfacry approach. ww 06:58, 6 October 2006 (UTC)
The flight restrictions are for public safety, not because they are high value targets - the FAA does not really expect terrorists to follow guidelines. 199.125.109.136 22:00, 18 June 2007 (UTC)

A smaller rectenna would be less costly, but requires a more intense beam for the same gigawatt power out. A more intense beam may be a problem for older aircraft, but new designs, can improve the Faraday cage which protects persons with pacemakers and most of the electronics. Traps to remove the beam frequency can be added, all this with very little weight penilty. Very large aircraft will reduce the power delivered by the rectenna for a few seconds, when they fly through the beam. Ccpoodle 02:40, 15 June 2007 (UTC)

[edit] Citations and Footnotes

This article now has 58 footnoted references, hopefully that is sufficient. Please let me know, I can hunt up some more if need be. Please be specific about what is missing. Thanks. Charles 03:00, 5 February 2007 (UTC)


[edit] It has been suggested that Solar mirror be merged into this article or section.

Solar Mirrors are not the same as Solar power Satellites. Please keep the pages separate. On the other hand the two pages should definitely be cross referenced and coordinated. I can see that there is some content on the Solar Mirror page which does not belong there and needs to be moved to the Solar Power Satellite page. I would be happy to assist with that task.Charles 15:24, 25 February 2007 (UTC)Charles 15:29, 25 February 2007 (UTC)

Concure with Cfrjlr here. Quite different underlying device / design. Similar because both invovle the sun and boht in orbit, otherwise, not much. Two different topics and so should be two different WP articles. ww 10:28, 9 March 2007 (UTC)

[edit] revision of solar mirror complete -- still less grounds for merge here

I have completed a major rewrite of the solar mirror page. At this point I think nothing further needs to be done, no need for any merge at this point. Thanks.Charles 19:37, 25 February 2007 (UTC)

[edit] solar cell vendors

It is important to validate the claim that high efficiency cells are actually available. there are very few vendors who offer the high efficiency cells, where do you get the number of "hundreds" of cell vendors? Most of the cell vendors have very low efficiency, the Spectrolab cells are the highest on the market that I have seen. It is not an advert as I have no connection with the vendor.Charles 05:46, 9 March 2007 (UTC)

It doesn't matter whether or not you're connected - please read the policy on external links, thanks. RJASE1 Talk 05:50, 9 March 2007 (UTC)

I have requested arbitration on the matter of the Solar power satellite page. There are many references to specific vendors cited throughout wikipedia.Charles 05:57, 9 March 2007 (UTC)

RJASE1 is correct here. It's not motive of the editor which matters but the content of the edit. In the case that the edit singles out the virtues of a commercial supplier, it is on its face, not WP material. I suppose I can imagine a favorable mention of a commercial product or company which would be acceptable, but I think such as situation will be quite rare. And would require considerable discussion before concensus. And thasame for disfavored products. WP has, and should have, no commercial ax to grind. ww 10:28, 9 March 2007 (UTC)
In case anybody wants to see, the MEDCAB (not ARBCOM) case is at Wikipedia:Mediation Cabal/Cases/ solar cell vendor citation. Veinor (talk to me) 14:13, 9 March 2007 (UTC)

What is the difference between Medcab and Arbocm?Charles

It is common to mention specific vendors and specific productsCharles 14:23, 9 March 2007 (UTC)

MEDCAB, the Mediation Cabal, is an informal way of getting an outside opinion on content disputes, such as this one. Any decisions it makes as to what editors should and should not do are nonbinding.
ARBCOM, the Arbitration Committee, deals with large issues, such as removing admin status from users. Its decisions are binding, and can be enforced by blocking users.
And just because it's common, doesn' mean it's right. The ever-changing nature of Wikipedia means that inferring style from other articles can be tricky, as sometimes those articles aren't written correctly. Generally, however, nobody will come down on you too hard for issues like this; people try to assume good faith. Veinor (talk to me) 14:40, 9 March 2007 (UTC)

When I get some time I will consult with the Solar Cell community and ask for their opinions on who are the most notable solar cell vendors with regard to efficiency. If a vendor is notable then it could have their own page, and be cited, right?Charles

[edit] advertising

Well, they can have their own page if they satisfy WP:CORP, sure. But that still doesn't make advertising them OK. Veinor (talk to me) 15:23, 9 March 2007 (UTC)

I thought we had agreed that my link to Spectrolab was not advertising. The reason for deletion has something to do with style, which I do not really understand. I read the guidelines and they make little sense. They are also being randomly enforced, there are many links to products and vendors all over Wikipedia.Charles 19:28, 9 March 2007 (UTC)

If there was a dirty pond outside of the back of your house, would you dump your sewage in it? No. The reason they exist is because either they are not the same sort of thing as the case here, or that they're wrong. Or, to use a more familiar adage, "If everyone else jumped off of a cliff, would you?". My point is that the fluidity of Wikipedia means that sometimes, people will base their decisions off of a bad precedent. This is also why citing precedent in arguments such as Articles for Deletion is a bad idea. This is also why they are being "randomly enforced". And the guidelines seem to make perfect sense to me. Veinor (talk to me) 21:12, 9 March 2007 (UTC)
I agree - the guidelines, while not always perfectly enforced (like any law or rule), are the only thing keeping Wikipedia from getting overrun by vanity and spam, and being totally discredited as a reliable source of information. RJASE1 Talk 01:52, 10 March 2007 (UTC)

[edit] Existence proof vs advertising

Surely in the special case of a technical and engineering feasibility question, like the practical availability of a product with a given performance at a given price, one should not reasonably argue against the admissibility of commercial specifications and availability information from engineering suppliers? The issue then is not commercial promotion, but the real, practical existence of the product. Citation of a few reputable suppliers must be permissible, as long as they are not singled out for praise or abuse, no? Wwheaton (talk) 03:06, 13 January 2008 (UTC)

[edit] efficiency

Energetic efficiency per se is irrelevant for this application. It's cost per watt (to buy the PVs) and kilograms per watt (to launch the PVs).WolfKeeper 19:11, 9 March 2007 (UTC)

Your comment makes little sense. Efficiency is important because it is linked directly to the other parameters which you do acknowledge are important, for example kilograms per watt is directly related to efficiency. You cannot therefore claim that efficiency is irrelevant.Charles 19:24, 9 March 2007 (UTC)

No, because for example some things you can do reduce the cost of the panel, even worsening the efficiency, and increases the weight but at the same time greatly increases the power per dollar. For example, the 'low efficiency' of many solar panels is actually due to the fact that they only absorb part of the solar spectrum. But a foil diffraction grating fitted to a solar panel would reflect a great deal of useless light away from the panel, except for those frequencies the panel can accept. The efficiency (which is measured from light power intersecting the power satellite to electrical power out) is actually lower, but the power generated per dollar goes up as does the power per kilogram (because foil is very light and solar panel is very expensive and avoiding irradiating the panel with useless frequencies avoids overheating the panel).WolfKeeper 00:23, 10 March 2007 (UTC)
For another example, many high-efficiency panels cost more to produce- they require extra processing steps. Even at high production quantities they still cost more than one that needs less processing steps. So efficiency is negatively correlated with cost/watt which is the primary metric people care about- ultimately that's what people pay for when the power comes out of their wall socket.WolfKeeper 00:23, 10 March 2007 (UTC)
Panel efficiency is not a significant metric for this application; light costs nothing. Area to put something costs nothing. Efficiency is only worth it if it improves one of the primary metrics. Sometimes reducing the efficiency improves these metrics.WolfKeeper 00:23, 10 March 2007 (UTC)

Most everyone is sort of correct. Most important is watts per kilogram, unless we can get the cost from factory to giant photovoltaic panel well below $220 per kilogram. A bigger panel to get the same nunber of gigawatts means more wiring power losses and/or lots more kilograms of copper. Automated repair of shorted or open cells is also an imporant consideration. We have a good idea how long low efficiency cell will last in space, but the new design, high efficiency cells may fail more often, or abruptly after a decade or two of use. Use of mirrors to concentrate the energy likely means the photovoltaic panels will overheat, unless active cooling is added to the design. In the vacuum of space, we have only radiation to dispose of waste heat. On Earth's surface conduction and convection are helpful in disposing of waste heat. Ccpoodle 22:31, 3 July 2007 (UTC)

[edit] Units of Energy versus Power

Units need to be kilowatt-hours, NOT kilowatt per hour. Kilowatt = 1000 Joules per second. My comment about "Watts per Second" was an "oops". Charles 02:55, 20 April 2007 (UTC)

[edit] Global warming danger?

Is there no danger of increased global warming due to increased amounts of heat coming from this kind of device (microwave hitting matter and heating it up)? which could probably be fine over the course of hours and days but over the course of years or decades? or are you assuming that these amount of energy and heat will be produced one way or another due to increased demand? 80.178.45.219 16:53, 7 July 2007 (UTC)Apollo365

This energy will be delivered to the Earths surface and will degrade to heat. What it will not do is be accompanied by exhaust gases (eg, CO2) which will trap solar heat in the atmosphere. The effect over time is considerable, and is exactly the problem we are facing just now. SPS energy will eventually reradiate and so have no long lasting effect. Likewise for other types of non fossil, none carbon oxidation energy sources. It's a critical difference and quite important. ww 07:15, 17 July 2007 (UTC)
If it is in L1+ position it would actually act as a sun shade and reduce total energy flux on to the earth.--BerserkerBen 01:09, 9 July 2007 (UTC)
Not really. Shading provided by SPS would be negligible. The shadow cast by the SPS would a) most of the time not impinge on Earth for about 99.99% of the time, and b) when impinging on Earth, would cover only a small area on the Earth's surface. Charles 15:44, 21 July 2007 (UTC). also, the angular size of the SPS in the sky would be tiny compared to the angular size of the solar disk in the sky, people on Earth would not even notice an SPS passing in front of the Sun, you would need a telescope to see the tiny dark spot against the bright solar disk, a little bit like a transit of the planet Venus in front of the Sun. Charles 15:46, 21 July 2007 (UTC)
However, locating it at the L1 Lagrangian would be approximately 1,500,000 km from the Earth, 42 times farther away from a geosynchronous orbit making aiming that much more difficult. Most space stations are going to be solar powered, but I do not expect that beaming that power around here and there will ever be useful. The flux available at the surface is a thousand times what we need. Covering just the Sahara Desert with photovoltaics generates 54 times total current energy used, of all types. Just covering every roof with photovoltaics provides most if not all of our electrical need, and it is a lot cheaper to slap photovoltaics on a roof 5 or 10 m up than it is to haul it 36,000 km up into outer space, not to mention maintenance - what did you intend to do with all the old panels a hundred years from now, just leave them there cluttering up outerspace? Let them burn up on re-entry? What a waste either way. At least on earth they can be easily recycled. 199.125.109.82 02:35, 17 July 2007 (UTC)
Solar Power Satellites will not increase global warming, they will decrease it. Global warming is caused by greenhouse gases capturing heat and holding it in, preventing the heat from radiating to space. Waste heat from SPS and any other source (e.g. nuclear, fossil fuels etc) will normally radiate out to space, so the global temperature would not increase regardless of the amount of heat injected into the atmosphere. Only greenhouse gases cause the temperature to increase, the heat input makes no difference. And furthermore, waste heat from SPS will be much less than the waste heat from coal, oil, or nuclear, because SPS rectennas operate at much higher efficiencies.Charles 15:34, 21 July 2007 (UTC)

[edit] Merge/pull

There's a fair bit of relevant content over on Space solar power. Also, I forgot about this page and created a bunch of redirects for alternate names pointing to it.... --Belg4mit 20:49, 6 November 2007 (UTC)

[edit] Remove extra links

I propose removing the "Space-Based Solar Power Efforts" link because it's an essay with a subset of the information in this article, no credentials, and no sources. Also "Environmental Community & Alternative Energy Information" because it doesn't have anything to do with SPS. If there are no complaints about this I'll go ahead and delete them in a few days. Wronkiew (talk) 20:34, 21 November 2007 (UTC)

Done. Wronkiew (talk) 15:07, 26 November 2007 (UTC)

[edit] Confusion about antennas

As well, to minimize the sizes of the antennas used, the wavelength should be small (and frequency correspondingly high) since antenna efficiency increases as antenna size increases. But, higher radio frequencies are typically more absorbed in the atmosphere than lower radio frequencies.

This part mentioned in the article seemed contradicting or isn't stated very clearly so I was wondering if it might be an error or if someone could phrase it better. —Preceding unsigned comment added by 75.138.21.242 (talk) 23:34, 6 February 2008 (UTC)

The angular beamwidth, W, of an antenna is roughly 1/N, where N is the numerical aperture, the diameter of the antenna in wavelengths at the frequency of operation, and W is measured in radians (1 radian = 57.3 degrees, approximately). Wwheaton (talk) 03:34, 13 February 2008 (UTC)
Ooops, I see that I was not quite right about the definitions of numerical aperture used in optics. I have modified the antenna section in the article to be more clear, and correct (ie, don't go there) on this point of terminology. Details of various definitions used in optics may be found in the link given previously. All are essentially equivalent, up to the factor of proportionality standard in various subfields. Wwheaton (talk) 04:01, 13 February 2008 (UTC)