Light & Depth

[daytonians]

I scraped my glass with a razor blade just prior to taking my readings. I do agree, that it is possible for very deep tanks to benefit from the principles in the articles, but they would have to be greater that 24 inches deep to see this is practice. Most tanks are less than that.

Since I would personally like to have a 36+ inch deep tank, this is of interest to me. I hope the theory is verifiable, but so far it isn't.

 

[JoeESSA]

In radio communications there are strong analogies. Consider a point source radiating out in all directions (a sphere). In this case we know that the energy density decays according to 1/R^2. Now consider a reflector behind this source forcing radiation out only over a hemisphere, 180 degrees. The "gain" at any given distance from the source is 2x compared to the spherical scenario. I.e. double the energy will be received at any distance from the source compared to the spherical scenario. However, the 2x energy density will still decay according to 1/R^2 or 2/R^2 relative to the spherical scenario. If we take it further and make the source even more directional using a different reflector the "gain" will become greater. E.g. you may have a very directional reflector giving say 20x gain compared to the spherical scenario, but the rate of energy density decay will following 20/R^2 compared to the spherical scenario. So, a measurements of energy density at different distances from the source will still obey 1/R^2 irrespective of reflector type and aperture.

Now, light from a tube as opposed to a point source does not just radiate directly perpendicular to the tube surface, but radiates in all directions. However the light energy will be greatest perpendicular to the tube and will decay gradually as the angle from perpedicular decreases. Ultimately it will be close to zero at zero degrees angle w.r.t. the tube. This is analgous to a dipole radio antenna. Mathematically this has a 2x gain relative to a point source antenna. Nevertheless the rate of decay of energy still obeys 1/R^2. In fact the tube energy density will obey 2/R^2. I.e. 2x gain compared to a point source.

This is all true in the air, but what happens to the light when it enters the tank with any of these light sources...Then we have the previously discussed light guiding effect due to internal reflection. This is similar to a microwave waveguide. Now it would be interesting to see light measurements made in a deep, totally empty aquarium with very clean glass. In this scenario we would not see energy density decay according to 1/R^2 w.r.t water surface, but in practice we have many, randomly shaped objects in our tank, so we have varying degrees of light absorption by objects, have scattering off objects as well as reflection from the glass walls. In the radio business the rate of decay of radio energy in a complex environment (e.g. urban environment) follows roughly 1/R^4 decay.

Not sure if that helps this discussion :rollface:

 

[JoeESSA]

OK, thought about this more. Here's the deal. The more a light source above a tank is focused downwards, due to using a reflector or different shape of bulb, the less light will be reflected of the glass. This means that the more directional the light source is then the light intensity at a given depth will predominantly follow 1/R^2.

The light sources used for our aquarium do not provide equal light intensity in all directions. In fact they are intentionally designed to be directional - to throw as much enery as possible in the direction we desire (or our corals desire).

There will ultimately be a transition from 1/R^2 to lightguide in a totally empty tank. However the depth at which this transition occurs depends on the angular distribution of the light energy from the source versus the dimensions of the tank. This will be true irrespective of the whether the light bulb is a point source, a tube, or a zingzangagon....Ahhh Ureka!!

 

[Cuervo]

<a href=showthread.php?s=&postid=8278958#post8278958 target=_blank>Originally posted</a> by daytonians
OK, being a photographer, I have a camera that can be used to check the level of light that is reflected off live rock.

Tonight I tried to duplicate the experiment in the article. I turned off my MH light, leaving only my PC lights which cover the length of my tank. I then check the light level at the top parts of the live rock, which are about 8 inched from the surface. Looking for similar looking sections of live rock at deeper depth, I took more readings. In ever place that I checked, the light had dropped off significately.

At a depth of about 18 inches the light measured 1/2 of the first measurements.

The top rock measurements were at ~ 8" deep. The lights are mounted~ 10 inches about the water surface. That is 18 inches from light source.

The measurement at 18" depth would put the measurement taken 28 inches from the source.

According to the norm of light decreasing by 3/4 every time the distance is doubled, this would be about right.

Consider that with your camera, you are measuring the light that is passing through the glass and the light that is being reflected from the rocks.

Between those two variables, it's not that great of a test for the discussion.

It's worth noting that as the angle of incidence increases (you go deeper into the tank) more light is reflected back into the tank, and less passes through.

You may have only been seeing the effects of that angle becoming greater and greater. - More light reflecting back in, less light passing through.

 

[JoeESSA]

Cuervo, see above postings. I'm now pretty sure that light will decay as 1/R^2 for most practical aquariums..

 

[pjf]

Misapplied Formulas

Misapplied Formulas

The 1/R^2 light dispersion formula only applies to a point source of light without its reflector. The 1/R light dispersion formula applies to a tube source, again without its reflector.

Rays of light are parallel when they leave a perfectly parabolic reflector. If you want to apply the dispersion formulas to imperfectly reflected light, you must find the distance to the “virtual” source. Take two rays of light emanating from the reflector and determine where they would have had to originate from if the reflector was not there. The distance to that “virtual” source is the distance you should use for “R.” If the rays are parallel, “R” is infinite. Even if the reflector is not perfect, you will find that “R” is much longer than the few inches between the lamp and the aquarium. It is as if someone raised your lamp far above the water without diminishing its intensity.

When the light from the reflector strikes the water’s surface, they are again bent towards the vertical by Snell’s Law and become near-parallel. When you take these near-parallel rays of light and again find the distance to their common “virtual” source, you will find that “R” is greater still and dwarfs the depth of the tank. With this new “R” inserted into your formulas, your calculations will indeed show that light intensity does not diminish much when you add the tank depth.

This light will head straight to the bottom. Light that does strikes the glass will do so at an angle shallow enough to be internally reflected and continue towards the bottom. Per a previous post, if the light in the water strikes the glass or plastic walls at an angle greater than 49 degrees from perpendicular (or less than 41 degrees from vertical), there will be total internal reflection (TIR). At such an angle, it will be uncommon to take more than one “bounce” to reach the bottom.

To achieve TIR, the light entering the water must strike the water at an angle less than 60 degrees from vertical. This is easy to achieve even without a reflector. Measure the length of your aquarium, divide by 4, and mount your light at least that height or higher over the center of your tank. When the light strikes the water, it will be bent to less than 41 degrees from vertical (Snell’s Law). It will then strike the glass at greater than 49 degrees from perpendicular and achieve TIR.

If light at the bottom of a home aquarium is less than that nearer to the surface, the culprits are likely to be the reflector, the water quality, the cleanliness of the glass or something other than the depth. If you have live rock that will absorb light, you will need to depend less on light reflecting off the glass and more on parabolic lamp reflectors that can direct parallel light downwards.

I surmise that one problem is that spotlighting is used in many aquariums that can only illuminate a portion of the tank. If you do not have uniform illumination, it is difficult to measure the total amount of light passing through each layer of depth. A single reading will not be representative of the light at that depth.

 

[JoeESSA]

Pjf,

Your maybe right. All the radio communications analogies I was trying to use apply at large distances from the source. So, I was probably "off" with all that theory...

For aquarium lighting the distributed nature of the light source (whether a tube or a metal halide bulb with reflector, etc.) cannot be ignored since the depth of the aquarium is usually no more than 3 feet. Agreed 1/r will apply to a tube, at least at relatively short distances from the tube.

On the subject of spotlighting consider that we rarely use parabolic reflectors that give close to parallel light rays. A MH bulb with parabolic reflector resulting in close to parallel light rays would have to be unreasonably large. In practice you can clearly observe a cone of light in the water coming from a metal halide bulb with typical reflector and in fact they are designed such that they can cover apprx 2 feet x 2 feet of tank area. These cones of light have fairly large solid angles, dÙ. I.e. they spread out fairly quickly - even when refracted towards vertical in the water.

An interesting relationship with illuminated area and solid angle of a cone is dÙ = dA*cosö/r^2 where dA is the size of the illuminated area at distance r from the source for a given solid angle dÙ. If the illuminated area is perpendicular to the radius r it simplifies to dÙ = dA/r^2. Notice the 1/r^2 relationship with distance. This equation still applies to a point source, but nevertheless a metal halide bulb with a typical reflector, whilst not a point source, is a divergent light source, i.e. the light spreads out with distance and entails a loss of light energy per unit area with distance. Let's assume a quick example where the MH reflector is 0.5ftx0.5ft and it manages to illuminate an areas of 2ftx2ft at the bottom of a tank. This entails (2x2)/(0.5x0.5)= 16 fold drop in light intensity at the bottom of the tank relative to intensity at the light source. If we were to illuminate a 2ftx2ft area with a parabolic reflector giving parallel rays then the reflector would have to be 2ftx2ft in maximum radius at the base. It would also have to be quite tall with the bulb set quite far up into the reflector, probably impractical. In any case whilst doing this may result in uniform light intensity with depth, your original light intensity at the source would be 16 times lower than with a 0.5ft x 0.5ft reflector....

Food for thought...

 

[pjf]

Light Motel: checks in but doesn't check out

Light Motel: checks in but doesn't check out

In your example, a spotlight illuminates the entire bottom of the tank but only lights 1/16th of the top layer of water. Despite the uneven illumination, the amount of light reaching the bottom is nearly equal to the amount of light passing through the water’s surface. They differ only in the distribution of light. Because water does not appreciably absorb light at aquarium depths, almost all the light will reach the bottom.

Here is a more realistic example:

• A metal halide pendant with a 0.5’x0.5’ reflector is mounted only 8 inches above a 2-foot cube tank. The water’s surface is entirely illuminated.

Although the water’s surface is entirely illuminated, it may not be with uniform intensity. The center may receive more light than the corners. Because light striking the water does so at less than 60 degrees from vertical (and strikes the glass at less than 41 degrees from vertical), total internal reflection (TIR) is achieved and light loss is nil. Because the light is mounted close to the water, dispersion is more rapid. The light rapidly becomes more uniform with depth. I submit that the light intensity at the center bottom of this tank will not be appreciably different from that of a tank half a foot shallower or deeper. The same lighting will work.

 

[JoeESSA]

I agree with the first statement that total light energy through the 1/16th area at the surface would be very close to the total light energy at the 2'x2' area at the bottom. The total flux is unchanged. You maybe understood this, but my point was that in this example the light intensity would nevertheless diminish. If total light energy is I, then we have a light intensity of I/(0.25) or 4I at the surface, but I/(2x2) or I/4 at the bottom. Light intensity is what people are measuring with light sensors, not total light energy. Light intensity is also what matters for a coral, assuming the coral is significantly smaller that the total area of the tank. Maybe the example was unrealistic in that the illuminated area at the surface was too small...If the illuminated area at the surface is greater, the more quickly the light will transition to a uniform light intensity distribution in the tank, assuming a totally empty tank.

Similarly, I also agree with 2'x2'x2' cube example you give and that there will be a certain depth where the light intensity distribution becomes uniform. Again assuming a totally empty tank. Many aquariums are set up so that only the front section of glass can provide reflection over the full depth of the tank. I reckon that some optical engineer or graphics programmer could model the different scenarios we are discussing and show where the light intensity transitions to a uniform distribution for a given tank geometry and maybe even what happens if only certain sides of the tank can provide reflected light. The biggest part of their job would probably be defining a representative light source. I.e. capturing the non-uniform nature of the light source.

 

[pjf]

Spotlighting

Spotlighting

It should be easy to spotlight only a portion of the bottom of an aquarium. The water’s surface bends light downwards so that it is closer to the vertical. Light passing through the air-water interface becomes “more parallel.”

Here are ways to enhance spotlighting:

• Use a metal halide pendant with a parabolic reflector approximately a half-foot in diameter. Design the reflector so the bulb is seated deep inside the reflector. This ensures that most of the light is reflected downwards and not dispersed via line-of-sight.

• Alternatively, one can utilize a dual-reflector system similar to that in a dental light. A small concave reflector below the bulb reflects light upwards to the larger main reflector. This ensures that all of the light emanates from the main reflector.

• Place the pendant closer to the water. This limits light dispersion through the air before it crosses the water boundary to be “refocused.”

Even if the light is not perfectly parallel, the air-water boundary will bend the light so that it is closer to parallel. Spotlighting an object at the bottom of an aquarium should be easier than spotlighting an object in air.

 

[JoeESSA]

No argument about that, spotlighting that is...

This has been an interesting thread. Just wonder where we stand now with regard to the original posting you made and the links to the articles on "no need for a higher power bulb for deeper tanks"?

Do we now reckon that this is true for all scenarios, or is this very setup dependant? The latter referring to type of light source, reflector, geometry of light source/reflector, distribution of light intensity of the light source, height above the water, geometry of the tank, objects in the tank, how many glass sides of the tank are available for reflection...If we could define a "typical" setup (i.e. the type of setup most commonly used) would that setup agree with the links in your original post or disagree?...

 

[Fredfish]

I have seen the numbers years ago, but do not remember the source. You could try old issues of Reefkeeping if you can find an archive and search for articles by Sanjay Joshi.

You could also try contacting Brian Plankis, the guy who wrote tha lighting article in the most recent rk mag. and get him to do a set of readings for this thread. I would only take him a mater of minutes.

Botom line, from memory, is that there is a significant dropoff from the top to the bottom of the tank. It is also not uniform as most reflectors are not all that good at distributing light evenly.

If you look at the old sprung & delbek book (vol1) you will see spectral absobtion charts for water. Water absorbs a lot of light energy and this is why high wattage lights heat our tanks so much.

 

[pjf]

Update from Mr. Huntley

Update from Mr. Huntley

This has been a very interesting thread for me as well. I wish I have answers to your very excellent questions. When I started this thread, I asked for more information but still haven’t found any beyond the original 1995 posting by Wright Huntley, who is active in the San Francisco Bay Killifish Association and has published in www.aquarticles.com. I did manage to contact Mr. Huntley yesterday and here’s what he wrote to me (October 10, 2006):

Freshwater is more transparent than reef water, to a slight extent. The
arguments really go astray, though, by introducing other variables
without understanding what is really happening.

Eliminate a few variables. Clean tank with clean fresh water and a
perfectly still surface. Clean glass and any darned kind of light you
want to put over the tank.

Light that strikes the surface at right angles continues downward in a
straight line. Light hitting the surface at any other angle is bent down
partially toward the normal incident rays, At the critical angle, light
inside the tank is propagating at roughly a 45 degree angle from the
surface. Those rays were nearly parallel to the surface before entering
the water and being bent downward. It turns out that this is just the
right angle for those extreme rays to also be 100% reflected by total
internal reflection from the glass-air interface.

The only way much light can escape the tank, that has gotten into the
water is if the surface is disturbed. Ever notice the bright shimmers
near the base of an active tank? Those flickering bands on the table are
the only possible way you can see the lamp over the tank, while looking
through the glass.

Get down beside your tank and try to look up and see your lamps through
the glass tank sides. Notice that it cannot be done if the surface is
really still.

1/R^2 has nothing to do with this situation. It only applies to a point
source in free space. The water surface properties alter the light from
any source to make the light that gets into the water experience TIR all
the way to the bottom.

Light leaves the tank by scattering from structures, plants, substrate,
dirt, fish, etc. Until it is scattered thus, it will propagate down
through the tank with only the normal absorption loss of water. Since
this is higher in red than blue, normal photometers may give wacko
results. You must specify the spectral content and allow for simple
water absorption before doing the measurement. That is still only about
5% per meter, in the red, as I recall. [That's why reef colors at 15-20
meters deep are so blue-green.] Water absorption is virtually
insignificant in any tank shallow enough to do maintenance on it in
street clothes.

Shading and reflecting light out off objects in the tank are the
significant factors in light being lower at depth than near the surface.

Wright

 

[JoeESSA]

Shading and reflecting light out off objects in the tank are the main factors in light being lower at depth than near the surface

That will be a factor in the practical aquarium as we have discussed. I.e., objects in the tank, how many glass sides of the tank are available for reflection.

I wonder if he is talking about total light energy or light intensity at a given depth? If he is meaning light intensity then I still think that the other factors we have discussed need to be considered. I.e., light source and reflector geometry resulting in a given light intensity distribution, height above the water versus geometry of the tank. E.g. I cannot see a single metal halide pendant (say 0.5'x0.5' reflector) a few inches above a 6' long tank giving a uniform light intensity distribution at the bottom, even with a totally empty tank, unless that tank is very deep. That's why we distribute the light source by adding a pendant for every two feet of tank.

 

[JoeESSA]

Also for 6' long tank, empty, still water, single MH 0.5'x0.5' reflector scenario I gave above I think we would see a significant drop-off in light intensity with depth. Of-course the light intensity at the surface would also be a strong function of x-y location (non-uniformity). Point being, it's as Fredfish said we cannot achieve a unifrom light source above all aquariums in practice. Having said that it would be interesting to see measurements from a high power LED array above a tank. That's probably as uniform as it gets...

 

[pjf]

Taking Advantage of Refraction and TIR

Taking Advantage of Refraction and TIR

Per Wright Huntley, “Shading and reflecting light out off objects in the tank are the main factors in light being lower at depth than near the surface.” The reasons cited include TIR and the transmission of light through water at aquarium depths. These factors allow a standard aquarium to act as a waveguide. There may be ways to take advantage of the way light behaves in an aquarium.

One should not shy away from deep aquariums for fear of higher lighting expenses. If lighting is adequate for the substrate of a standard home aquarium, then it may be adequate even if another several inches of depth is added. One example is a 30-gallon breeder (36”x18”x12”) versus a 65-gallon (36”x18”x24”) where one is twice as deep and can support twice the fish.

Total internal reflection (TIR) can be used to retain light that would be lost through the glass or acrylic walls. TIR can be achieved with reflectors that direct most the light downwards and by mounting the fixture at a height at least one-quarter the width of the tank. The key factor is that light strikes the water’s surface at an angle no more than 60 degrees from vertical. The light will be refracted to less than 41 degrees from vertical and be totally reflected by the walls.

Without parabolic reflectors, a light fixture should not be mounted too high as light dispersion is greater in the air where the 1/R^2 rule predominates. At the water’s surface, light is refracted towards the vertical and its dispersion is “locked in” by this refraction and by TIR. An aquarium will not disperse light as much as air. It transmits and reflects what is received at the surface to the substrate below. If the substrate at one portion of the tank receives greater illumination, it is probably because the surface above it received greater illumination.

Pendant lighting seems to be a better match for hexagonal tanks than for rectangular ones. When a single pendant is suspended above a 6-foot long but narrow width tank, more light is received by the water’s surface at the center of the tank than at the corners. The waveguide effect is stronger at the narrow center of the tank because the front and back reflective walls are closer to the pendant and assures TIR. If light strikes the left and right aquarium walls at too steep an angle, that light will be lost through the glass.

When it is desirable to spotlight a portion of the substrate, refraction and reflectors prominently come into play. The air-water boundary refracts light closer to vertical and can be used to keep a column of light from dispersing rapidly. This effect can be enhanced with parabolic reflectors, recessed bulbs, dual-reflector fixtures, fixtures that are mounted close to the water, or proximity to the reflecting walls. In the case of hexagonal tanks or narrow tanks, the walls may be used with pendants to focus reflected light at portions of the substrate. Again, make sure the light strikes the water's surface at less than 60 degrees from vertical.

If uniform lighting is desirable, multiple pendants, tubes or LED arrays can be used. Uniform lighting at the surface and reflected light can be used to retain both light uniformity and light intensity at the substrate.

 

[pjf]

Only 14% Loss in 2-foot Tank?

Only 14% Loss in 2-foot Tank?

<a href=showthread.php?s=&postid=8319848#post8319848 target=_blank>Originally posted</a> by Fredfish
I have seen the numbers years ago, but do not remember the source. You could try old issues of Reefkeeping if you can find an archive and search for articles by Sanjay Joshi.

You could also try contacting Brian Plankis, the guy who wrote tha lighting article in the most recent rk mag. and get him to do a set of readings for this thread. I would only take him a mater of minutes.

Botom line, from memory, is that there is a significant dropoff from the top to the bottom of the tank. It is also not uniform as most reflectors are not all that good at distributing light evenly.

If you look at the old sprung & delbek book (vol1) you will see spectral absobtion charts for water. Water absorbs a lot of light energy and this is why high wattage lights heat our tanks so much.

High wattage lights heat our tanks because light is absorbed by the substrate, not by the water.

Sanjay Joshi did indeed write an article entitled “Underwater Light Field and its Comparison to Metal Halide Lighting.” It was published in the August 2005 issue of Advanced Aquarist’s Online Magazine and portions were reprinted in volume 3 of The Reef Aquarium by Delbeek and Sprung.

In the article, Joshi states:

“Most of the SPS and other corals in our reefs are found in waters less than 15-20 meters deep, but our reef aquariums are usually only 24 to 30 inches deep. At this depth of water, the amount of light lost to absorption by the water is quite small.”

While Joshi astutely observes the low light absorption by water, there is no mention of the bending of light towards the vertical by the surface (Snell’s Law) and there is no mention of total internal reflection (TIR) by the aquarium walls.

Joshi posts two charts in his article to show that 2 feet of water will attenuate light by 14% (4% to 33% depending on wavelength). Referring to one of his charts, Joshi writes:

“For the Iwasaki lamp at 6" from the water surface, the loss due to 2ft of water is about 14%, where as the loss due to the change in distance from the source (from 6" to 30") is about 70-90% based on the inverse square law of light and depending on the reflector being used. In practice this loss will be lower due to the additive effect due to multiple lights, but will still dominate the light loss as compared to loss due to attenuation in water assuming clear water similar to the ocean.”

Here are my thoughts about his conclusions:

• Using Joshi’s measured figure of 14% light loss in two feet of water, this means that each foot of water transmits 93% of light (1.0 â€"œ 0.14 = 0.86 = 0.93 x 0.93). If our tank is 1 foot deeper, the light loss at the substrate would be another 7% (1.0 â€"œ 0.93 = 0.07). An additional 7% light loss at the substrate due to a 1-foot deeper tank does not automatically mean that additional lighting is required.

• Using the inverse square law and no reflector, the calculated loss of moving from 6” to 30” away from a point source of light is 96% (ratio of 1/30^2 to 1/6^2 = 4%). Joshi’s expectation was that he would lose 70-90% of the light depending on the reflector. Yet, he only measured a loss of 14% in 2 feet of water. This lower than expected loss of light is proof that the inverse square law should not be blindly applied across a refractive surface. The calculation of R in this formula should be based on the “virtual” distance to the source.

• Joshi notes that there is room for improvement. Had he used a parabolic reflector or mounted his light differently to take advantage of total internal reflection (TIR), perhaps he would have measured a lower loss than 14% in a 2-foot deep aquarium.

 

[JoeESSA]

Interesting. Does he say how he was performing the light measurements?

BTW, light bulbs produce a substantial amount of IR, especially metal halides. The lower IR wavelengths will be readily absorped by the water. I think that this would be the most significant factor causing the water to heat...

 

[Fredfish]

Thanks for the link pjf. I missed this article.

I always thought that the effects of a reflector in capturing and redirecting light into the tank would be greater than what is shown by this article.

I think that Sanjay actually separated out the effects of light loss so that after applying the 70-90% loss due to inverse law, a further 14% was lost due to absorption. That the way I read it anyway.

Sanjay also seems to think that we can gain a lot of light using a white sand bed. I wish he had quantified 'significant'.

I stand by my original statement that a lot of light is lost from the top to the bottom of an aquarium. It appears from Sanjay's article that most of this loss is due to the invers square law though.

Fred

 

[pjf]

<a href=showthread.php?s=&postid=8369369#post8369369 target=_blank>Originally posted</a> by JoeESSA
Interesting. Does he say how he was performing the light measurements?

BTW, light bulbs produce a substantial amount of IR, especially metal halides. The lower IR wavelengths will be readily absorped by the water. I think that this would be the most significant factor causing the water to heat...

You are right in thinking that the red end of the spectrum is absorbed more readily by water. In his article (www.advancedaquarist.com/2005/8/aafeature), Joshi states “the amount of light at 700nm absorbed by 2ft of water is 33% of light just below the surface. For light at 400nm this is only 4%.” The light spectrum produced varies by the lamp. His measurements of the Ushio 400W 10000K lamp show a significant drop in output at the red end of the spectrum.