Arc Length Limitations, Arc lengths effect on light into triplet Options

[pagercam]

First off let me explain that while I'm an engineer with a few more years of experience than I care to admit (yes, I'm old) I don't have much expereince in optics. But I was wondering how we could evaluate the effect of arc length on the amount of light getting into the triplet. I've had to make some simplifying assumptions so this may not be entirely valid but I think that I've discovered some useful concepts that might help others in their lamp selection and PJ design.

Arc length has been mentioned here in LL but rarely quantified, this characteristic is only sometimes included in bulb datasheets. It is certainly logical to beleive that shorter arc lengths being closer to point light sources, should work with the fresnels and spherical reflectors that assume point sources better than a long arc or filiment. Light not coming from the focus point should get though the fresnel but is it useful to the image? Points near the arc will probably still be useful but the effectiveness would be expected to drop off the further away we get from the focal point.

So I started playing with ideas in the RAYTRACE program. Below is my test case, in which I assume a 37mm arc (the length in the bulb I planned to use). Vertical black lines marked 18.55 are the two halves of the arc. The two vertical pink lines in the middle are the 220mm fresnel on the left and 330 on the right, the horizontal dashed lines show the focal points and are dimensioned 220 and 330 respectively. The 50mm vertical line on the right is the rear lens of the triplet at 320mm from the 330mm fresnel as specified in the LL plans. The red lines (rays) represent the light coming from one end of the arc, green the middle and blue the other end of the arc. Each of these 3 points has rays going to the center, outside and half way point of the fresnel to show the range of angles involved. I expected it to be difficult to keep track of where the light ended up after the two fresnels, but as can be seen the rays converge to points on the other side of the optical axis. So light starting at 18.5mm above the optical axis on the 220mm side, converges to a point 28mm below the optical axis on the 330mm side at 330mm. So the ratio of the fresnels 330/220 = 1.5 means that a point starting at 18.5 x -1.5 = -28 (it doesn't come out exact because I didn't align the model perfectly, but you get the idea).

 arc37.gif ( 10.26K ) Number of downloads: 54


So given our 220/330 fresnel pairing the effective arc length will get multiplied by 1.5. I assumed a 50mm triplet side as I don't know the exact dimensions. 28 + 28 = 56mm so not all the light will be captured by this triplet. So atleast some of the light form the 37mm arc will not get into the triplet and FOV will force us to get light into an even smaller area.

[pagercam]

Next I modeled the "Ultimate Light Kit" as sold by LL because I knew that it had a 27mm arc that should fit within my theoretical 50mm triplet optics. Here is the model of that.

 arc27.gif ( 20.8K ) Number of downloads: 49


While the focal point of the ends falls within the range of the triplet some of the light is will not make it into the triplet. I have added a red ray to the bottom of the fresnels to show the full range of the light from the top end of the arc and this light would hit the side of the triplet and not enter the optics.

[pagercam]

That not quite being the solution that I was looking for I modeled a 20mm arc as seen here.

 arc20.gif ( 9.7K ) Number of downloads: 43


As can be seen from this model all the light appears to enter the triplet so this is the best case yet. There may still be FOV problems with the rays at the extreme edges but atleast this seems to suggest that we want/need bulbs with a 20mm arc length or less. This is not to say that a 27 or even 37mm arc length bulb will not work as many LL members have shown great results with various bulbs (The EYE PS bulb has a 44mm arc).

I think it can be suggested that roughly the same amount of light is generated at each point along the arc so we could say that 1/37th of the total lumens produced by a bulb (with 37mm arc) would be present in each mm of arc length (this is a guess not a fact). So if only the light from the center 20mm (used as an example) can get through the triplet then only 20/37= 54% of the lumens would contribute to the image brightness. The bulb I was planning to use is rated at 29,000 lumens (I selected this bulb for color temp more than brightness) . Given these assumptions only 15,675 lumens could be used (before considering the limited angles of light that actually hit the fresnel). But a 250W bulb with a 20mm arc generating 20,000 lumens would start off with 20,000 lumens that would contribute to the brightness. Everything else being equal the resulting image should be 20,000/15,675 =1.27 or 27% brighter even though the bulb is rated at 68% of the brightness.

Now I've made a lot of assumptions here so don't take any number too seriously but I think it is safe to say that the effective arc length is increased by a factor of 1.5 (given the 220/330 fresnel setup) so arc length should be less than 2/3 of the rear lens of the triplet and smaller than that to account for FOV issues.

This also suggests that the PRO lens triplet at 100mm should be able to make use of longer arc lengths than the standard triplet, so suggestions that larger lenses let more light through would be correct and have an actual basis in fact.

You can still use any arc length you want, but you might not get all the lumens you expect.

[DAZZZLA]

Here are some things that you may not have considered.

I think the standard triplet is a bit bigger than 50mm.
The physical length of the triplet body will block rays.
The arc can be adjusted to direct the rays to pass through the centre of the triplet. (Must be kept to a Min to preserve the arc image)

This also suggests that the PRO lens triplet at 100mm should be able to make use of longer arc lengths than the standard triplet, so suggestions that larger lenses let more light through would be correct and have an actual basis in fact.

The original pro fresnel that were 790mmFL would have a ratio of 790/220= 3.95 so for an arc size of 37mm it would project an arc image of 132mm. This is one of the reasons that they didn’t work. The new fresnels that are 650mmFL will have a ratio of 2.95 and a projected arc size of 109mm. So a bigger aperture size doesn’t necessarily mean a brighter image, it is the fl and the aperture and it is referred to as the f/number in photography. I don’t believe that a larger lens, when used in projection, necessarily is better. As long as the arc image can pass though the lens it will work. Just as an example if you had a projector set up so that all the arc would pass threw a 50mm lens and then replaced it with a 100mm lens with the same FL it would have little affect on the brightness. All in all you are on the right track.

DJ

This post has been edited by DAZZZLA: Jul 14 2005, 11:18 AM

[Rox]

yes i agree mostly with you.
Anyway, the projected arc won´t be as precise as your drawings but a more diffuses arc zone (where a larger aperture lens would capture more light) but if we consider ideal world (thing that I like to think as a starting point of a design) then the arc lengh will determine the lens aperture, yes.

But the fresnell pair will determine the projected arc magnification, a 330 rear fresnell will help on that but the solid angle from the bulb will decrease that way, so we can think a condenser lens will fix thisproblem, but we find that the condenser lens will magnify again the arc lengh, so the virtual arc (the arc that is seen from the rear fresnell view point) needs to be considered on the design.

This needs to be considered on the ideal design, the 400W ushio lamp at here is stated 27mm arc gap.

[DAZZZLA]

but if we consider ideal world

[GadgetSmith]

I would be interested to see what results you get from using a 317mm field fresnel, which are the ones currently being supplied by LL, as they were designed to put more light into the triplet based on the split design.

[pagercam]

I realize that there are a lot of assumotions but I think what should be taken from this analysis is that there is an effective arc growth of 1.5 purely due to the fresnel FL ratio and this will mean that light from longer arc will not make it into the triplet. Exactly how much is hard to say but we are certainly missing some and short arc bulbs are the answer to this problem and this may be helped by going to lower wattage bulbs.

317mm fresnls will help some but the difference between 317 and 330 is less tha 4% so don't expect major benifits. The fact that the 317s are thinner plastic than the 330s probably makes more of a difference. I specificaly chose 330mm as I intend to use a 17" LCD are the 317s aren't large enough to cover a 17" LCD.

My next step is to look at arc length with the reflector and see what effects I can see there, I expect this to be worse and the error in position will get magnified by the reflection.

Another thing that I started thinking about last night is the fact that I placed the fresnels in a nonsplit configurtion and I expect that the offset angles will be worse given a split config, I'll post results.

This post has been edited by pagercam: Jul 14 2005, 05:02 PM