Hi,

I would like to share a model that DAZZZLA and I toyed around with a while back that I think sums up in simple terms what it is that a light engine is meant to accomplish. I think everyone should have a solid grasp of this before working out any light engine design as it answers some fairly complex questions in a simple way.

If you point your Pro Lens'ed projectors at a bright white diffused surface and take a look inside your projector you will notice something pretty cool: a circle of white light will be projected onto your bulb. If you remove the bulb and put a sheet of paper in its place you can get a nice solid focus of that circle at around 20cm from the Collimating (first) Fresnel. Which is very close to the 22cm Focal length of that Fresnel. The circle is in aqua blue in this drawing:

Click to view attachment

We are looking down at the projector from above. The Grey horizontal line in the drawing is the Collimating Fresnel. The Green line marks the 20cm dimension between the circle of white light and the Fresnel.

If you then measure the width of the circle, you should find it is around 2.25cm in diameter.

What the circle represents: Any wave of light that passes through the circle on its way to the Collimating Fresnel could project. In other words any light that passes through this circle could contribute to brightness of a projection.

But its better than that: Any wave of light that could have passed through this hoop, without regard for where it began could also project. What that means is if you extend any light wave that impacts the Fresnel to an infinite length, if that extension passes through the circle then you are dealing with a wave that could project.

However (and this is the key), any wave of light that does not extend back or forward through this hoop will not project.

For example: take a look at the gray and purple line segments scattered on the circle side of the Fresnel (horizontal Gray line). The gray lines represent sections of light waves that will not project, and the purple ones could project. We don't know where these waves started from -it doesn't matter. You will notice that the purple light waves can be extended to pass through the circle, while none of the gray ones can.

So that is the first part of the model. The second part of the model attempts to show which waves that impact the Field (Second) Fresnel could project. If you draw a line from the edge of the circle through the center of the Collimating (First) Fresnel, You have actually drawn the maximum incidence angle at which light can project when impacting the Field Fresnel. I have measured this angle to be about 3.2 degrees.

So looking at the gray and purple lines after the collimating Fresnel you can see the only ones that will project (purple) are within 3.2 degrees from The Normal (head on).


Hopefully this helps with the discussions.

For now, bear in mind that these numbers may be incorrect (they were gathered in haste), and this doesn't represent all the complexities. For instance, there is presumed to be another circle that says not only that light could project, but rather will project. Problem is, that circle gets gradually smaller the further towards the edges of the Fresnel that the wave segment of interest is going to impact. The size of that circle could be derived by pointing a laser pointer through the triplet such that its beam impacts the corner of the LCD inside while having the Laser pointer at as steep an angle as possible. Where that pointer projects within our previous circle is the edge of the second circle. But that all isn't what I wanted to get at here. Just the basic idea.

Also note that what I've presented here is the real world way (with an actual projector) to arrive at what can also be done with drawings. If there is any interest I could (or DAZZZLA) get those drawn methods up. But its a lot of work to beat the simple experiments above with a ray trace.

If anyone finds flaw with anything here, post away .

Mark

Sorry dont have any thing to add to it but I do have some ?s

20cm? this is acording to your rear fresnel (220mm) ?

This could also help align your pj componites?

So if i had a thousand bulbs all behind a 20cm opening (circle in shape) all the light that passed throught that hole and reaches the fresnel would be exceptalbe for projection????? Thousand being an exageration and assumeing that the ray also can continue to the wall (screen)?

I dont under stand what the black lines are? why are they not purpindicular?

The circle from above (straite above ie.) should not truely be visable but from the front should look like a circle?? yes no??? maybe?

Yes. The Focal length of the rear Fresnel defines this number. But to be precise, you pull the line from the half way point between your two Fresnel's. That is why it falls a couple centimeters short.
20mm would work. Not 20 centimeters, though.
The procedure takes care of this for you. By could project I mean it will contribute to the picture.
The gray line is the Fresnel. The black line is the work line mentioned in the procedure to establish the second part of the model (the maximum incidence beyond the first Fresnel). It is stretched from the edge of the circle to the center of the Fresnel.
Yes. It is not 3 dimensional. What I have drawn shows it tilted slightly, but in reality it is flat and parallel to the optics.

Mark

thx

looks real solid. but i got some other ?>

so if the lid of your light box is what lets the light out , the opening of this hole that lets the light out on your lid should only be 2cm apx. with the acompanying 220mm fl rear colminating fresnel?

this seam like it would block alot of light that could still be projected im not sure through and you seem to know alot more than i do, or will ever? but plz help me under stand

I see what you are saying, but by lid you must mean opening or gate of the light box? And one of the key points I was really getting at is that the origins of the light waves don't matter. The idea is, by using this model you can design the tolerances into light engines that pretend to send light from a single point (gate) but in fact do not. It also describes the tolerances needed such as when selecting LED's for an LED array, and exactly what your light engine must accomplish if you have no collimating Fresnel in the first place (for instance). So it really isn't about a real physical gate, but rather how to model what the system is expecting so you can trick it.

For example: Lets say I wanted to use an LED array in place of the Lamp and Collimating Fresnel. I have decided it would be best to create a grid of LED's the size of (and directly behind) the LCD Panel. Since I now know I cannot exceed 3.2 degree angle of incidence with the Second Fresnel, I would need to select LED's with no more than a 6.4 degree viewing angle to be efficient.

Or: lets say I want to use a 2 foot long florescent light tube in place of my Lamp. I now know that only the light waves that emit from the lamp that can be extended to pass through that circle (and still impact the Fresnel) will project. I would now discover very quickly why that is not going to be too efficient as-is .

Mark

Well done, Mark. This is a great summation of all the light engine threads I have seen.

Any wave of light which is not on a vector that extends through a 2.25cm diameter circle centered 20cm behind the Collimating Fresnel cannot contribute to the brightness of a projection.

It should be titled "Standard Projector Optics in Sentence" and stickied.

Thanks.

But I think the second part to the model is important as well since it defines what your goals are if building a light engine without a Rear Fresnel (LED, parabolic, etc). In other words, completely non-standard projector optics.

So the summation sentences are:

1. Any wave of light which is not on a vector that extends through a 2.25cm diameter circle centered 20cm behind the Collimating Fresnel cannot contribute to the brightness of a projection.

2. Any wave of light at greater than 3.2 degrees incidence with the second Fresnel cannot contribute to the brightness of a projection.

And then there is the third part that I just touched on:

3. A wave that does extend through the outer edge of the 2.25cm diameter circle and impacts the opposite outer edge of the First Fresnel cannot contribute to the brightness of a projection. Tricky for sure. This point deals with the usable aperture of the lens as the incidence increases. I decided to not go into too much detail with this. Just bear in mind there is another circle that defines an area where all the light that vectors through will project. It is smaller than the first. So put a different way:

3. Any wave of light which is not on a vector that extends through an (yet to be determined but smaller than 2.25cm) diameter circle centered 20cm behind the Collimating Fresnel cannot not contribute to the brightness of the corners of a projection.

Mark

Just wanted to ask some thing, burp. OK, So any ray not passing through this theoretical 20mm circle is not adding to the brightness of the projection and corners but are they detrimental to the projection or are they of no concern? Laymen's terms, do we want to block the light that does not pass through this circle?

My view is that any light that is not directly related to the image on screen should be blocked at its source. If it’s not practical to block it there then it could potentially cause problems, extra heat, lower contrast or other optical issues. It may only be a slight improvement to the image but an improvement is an improvement.

Is a logical progression to consider using a spherical reflector (with holes for the globe to extend out of) with a 20mm hole positioned where the circle is? Of course, this would block the rest of the light (per JackieChan's question).

Sure, but I figure that would be overkill and difficult to cool. You need to keep the sphere as small as possible to keep as much light in play as you can. Probably better off to just stick with a light gate in front of the light engine of your choosing.

edit: jackychan, why is there a Budweiser ad in your post?

Mark

Thanks for the clarification, Mark. I'm glad that we've got a specialist here to help with some of the more technical questions. Here are a few:

After reading the thread you linked me to it sounds like any of the light that's going to be used will be coming from a 2.25cm circle about 20cm back from the rear fresnel.

Should the lamp be placed so that the arc is right in the middle of that circle?
How big is the arc on a LL T15 lamp?
If the arc can't fit in the circle, is this why the ceramic lamps perform so well for their wattage? (because their arc fits in the circle)
Is this also why ceramic lamps are sharper than their quartz counterparts? (because they aren't producing light outside the circle)
..and finally..
If one were to use a light gate in front of a 400w quartz bulb would it be just as sharp as the smaller-arc'd ceramic bulb? (since light outside the circle would be blocked from reflecting off of something else in the box and causing a less sharp image)

Thanks! You really seem to know what you're talking about so I'm just trying to learn from someone who I'm certain will be giving the right answer.

I'm also curious to know if a smaller iris placed directly in front of the lamp arch would create a virtual smaller arch without sacrificing lamp wattage?

It would be nice if a piece of sheet metal with a hole drilled in the middle would make the image sharper. Such a simple mod, AND it would help block heat from the LCD too!

Yep.
It just fits. I don't have a bulb around right now, but I think it is about 2cm.
I would tend to think so. But specifically, both lamps will fit within the larger circle. The smaller lamps will fit within the smaller circle mentioned briefly in the thread. The smaller circle defines the area where all light will project -even at the edges of the panel. If you are trying to light the center of your panel, then the 2cm circle mentioned is the tolerance you need to stay within to project all of the light. But as you move outwards towards the edge of your panel, the circle gets smaller. What ends up happening is the very edge of your panel generates quite a small circle. All of the light within that circle will project. Anything outside will not (at the edges of the panel).

The ceramic lamps are probably staying within this smaller circle, so while the center of the projection may not be much different, the outer edges will be brighter than a larger arc.
It isn't that they are producing light outside the circle, that light does nothing. It is that by utilizing the full width of that circle, they are also utilizing the full width of the lens. Whenever you use the outer edges of the lens, you are not going to get as sharp a picture as if you use just the center. If we had enough brightness, you could actually place an iris at the lens that stops down the usable aperture (just like in a camera). But we don't. The best thing for us to do is to get the arc as small as possible.
Yes, but you would loose brightness from blocking the light that is withing the circle.
Again, the reason for the lack of sharpness is more from using the outer edges of the circle, and thus the lens.

Pretty cool how that simple model can answer all of that, eh?

Mark

Yes, very informative! Thanks so much for taking the time to explain all of this. It has shed light (pun not originally intended, but I'll go with it) on how much arc size really matters!

I guess what we've got to figure out now is how small that smaller circle is.

One more thing-- What's the size of the circle for the smaller standard triplet?

An 85mm aperture at the rear of a modded pro triplet works reasonably well. Placing the aperture inside the triplet would be better though.

DJ

No problem. It is satisfying that the model got you asking all the right questions.
DAZZZLA put together a very nice addition to the model that shows how to calculate this with drawings. What it lets you do is find the soft aperture of the lens with a drawing. I figure a nice experimental technique (without the laser mentioned in the thread) may be to place an opaque disc over the center of your lens. Have it so there is just a small gap of lens left over around the perimeter. Then shine a very bright diffused light in around that disc. I think that would theoretically project the size of the smaller circle at the bulb.
It is a bit bigger ( believe it or not) than the Pro setup. I think it was about 4mm more in diameter.

Mark

If the standard triplet has a bigger circle than the pro triplet, its inner circle would also be bigger, right? That would mean the standard triplet puts more light to the screen than the pro triplet? (given that both are using the same bulb) This would also mean that the pro triplet has more to gain (than the standard triplet) from a smaller arc'd lamp, right?

I guess I was under the false impression that the pro lens is more tolerant of a larger arc, when in fact it's the other way around!

One more question-- I imagine that circle gets smaller the farther away from the lens you go, so would it get larger the closer to the lens you go? (meaning to fit a larger arc into the circle you could just move the lamp closer to the front of the projector) There must be something wrong with that reasoning else people would have already done it, I just don't know what..

The true F vaule of the pro triplet should be slightly lower than the standard triplet so it will alow for a larger lamp arc and be brighter.

and once again i am confused

so the circle for the standard triplet would be bigger than the circle for the pro lens, but the pro lens has a larger diameter which more than compensates for its longer focal length, resulting in the pro lens having the larger circle?

i guess the circle for the standard triplet isn't really a few mm more than the pro lens's circle.

so.. the pro lens has a 24 mm circle, and people say LL's T15 just fits in the pro lens, so would the arc be 24mm? i'm surprised the arc length isn't listed in the LL shop..

and i'm still wondering what size circle the standard triplet has..

http://en.wikipedia.org/wiki/Aperture
f value means aperture, usually how "big" one lens is to another lens. its like spraying water through a hole in a wall. except with light it's light converging or diverging (a cone) and how much of the light the optics are able to affect due to limits of physical size.
in photography and in systems with an iris you can change the aperture with the iris which affects how much light gets though and how big the circle of confusion (depth of field) will be.
with the triplets and Fresnel's the light cones are different sizes because of the different focal lengths, hence different F value which is compensated by making the optics physically bigger.
standard triplet, shorter focal, wider "cone" angle
pro triplet, longer focal, smaller angle longer cone
if you had both a standard and pro lens projector you can put something right in front of the triplet (inside part of projector) and see the size of the arc when it hits the triplet. you can also go upto the screen, squint or use a black screen, and see the arc image by looking into the triplet. there are some other trics to see the arc for centering the lamp like putting a magnifier in front of the triplet so that you can see the arc image on the screen.

in a commercial PJ the imager is small vs the lens so they have small f values.

if you have a camera with full manual you can play with the F stop and see how it affects depth of field. you will have to compensate with shutter speed for the different F stops or use aperture priority mode to have the camera do it automatically. < you just learned photography 101

Is that because you'd be getting the maximum possible light and then just cutting out the parts that aren't needed, versus cutting out parts that would add to the whole if done by the bulb?

Having not taken apart a triplet yet, what are the temps like inside? I'm just trying to gauge materials to do it with.


I think this is why Elken was measuring the Lumen/mm of arc length. In that respect, the ceramics put out more lumens than a larger arc bulb (I forgot the actual numbers).


I think the reason that people don't go for closer bulbs (asside from the heat at that distance and lack of large (cheap) fresnels) is that there would be more hotspotting in the center. Perhaps with the use of a precon...

Nope. The soft aperture generated circle (the smaller circle) should be smaller for the smaller lens.
The circle represents a very specific point behind at the lamp. It doesn't exist anywhere else. The biggest problem with trying to explain the circle logic is that people automatically think I am talking about the lamp. While the real purpose to the circle is that we can use it to completely ignore where the light is coming from (like a lamp) and still know what works and what doesn't. You can't move the circle. It's size, shape, and location cannot be modified without modifying the projector. And there is only one circle.

If you moved the lamp forward (and went too far) you would not be able to extend all of your light waves back through the circle. The model is meant to tell you where you can place the lamp, and it shows exactly what would happen if you did move it forward.

Mark

Sure, if you shorten the focal length of the rear fresnel, the circle moves forward, so you want to move the bulb forward. And the closer you get the more uneven the lighting gets towards the corners. But moving the bulb forward without shortening the focal length would cause less light to extend back through the (still where the bulb used to be) circle.

Mark

So from what I've gathered so far..

1) The size of the outer circle is determined by focal length of the triplet
2) The size of the inner circle is determined by diameter of the triplet
3) Location of the circle is determined by the focal length of the rear fresnel
4) Moving the bulb closer to the panel (and thus using an appropriately shorter focal length fresnel) will result in a brighter image with more of a hot spot in the center
5) There is nothing to be gained by placing the lamp outside of the circle, so always keep it in the circle!

My projector is going in a room that does get a fair amount of ambient light during the day, so I'd prefer to go with the 220mm rear fresnel for higher light output. I'm thinking (hoping) that I can get away with this without too much of a noticeable hot spot since I'll be masking off the screen to 16:9.

Let me know how that goes.. I am planing on using the Standard triplet and fresnels, with the CDM 150w bulb, and a Samsung 730b LCD (17" 1280x1024 res) but will be using powerstrip to make the resolution 1280x720, and will also tape/board off the unused part of the LCD (To keep lightleakage and such low)

But mine will be in a room that sees next to NO light other than my lamps.

Anyway, goodluck

It is determined by the size of the triplet, and ultimately the ratio between the focal length of the front Fresnel and rear Fresnel.
It is determined by the size of the panel, and the soft aperture of the triplet.
Yes . Technically, you also want to subtract half the distance that separates your two Fresnel's.
Here's the kicker. The circles both get smaller the shorter the focal length of your rear Fresnel. So unless you can keep the arc within those circles (or do as well as you did before) you will not get to enjoy the increased collection benefit.
Sure. And if you can simulate light having come from within that circle, then you have done just as well.

Here is how you work out the size of the outer circle (the hard aperture circle is what we named it) graphically:

Draw a line from the edge of your triplet, from the middle (of the length) of the triplet. Make that line pass through the mid point between your two Fresnel's at their centers. Where that line intercepts the focal length of your rear Fresnel (minus half the distance that separates your two Fresnel's) is a point on the perimeter of the circle. If you look at it, you can see how the ratio between the various focal length's really matters.

Mark

If what you want is to maximize the size of the circle, then you want to get the biggest triplet you can with the shortest focal length while still having a wide enough Field of View (large soft aperture) to image your entire panel width. Then you want a Front Fresnel that matches (actually slightly exceeds) the focal length of that triplet. Then you want the longest Rear Fresnel possible. Each of these above factors contribute to the having the largest circles possible. Which is of these factors is the most important would need to be modeled.

The problem is that we have an important requirement of keeping the bulb as close to the rear Fresnel as possible. So the only way extending the focal length of the rear Fresnel would work is if you compensate for the light spillage with an improved light engine. The great thing about having a larger circle is that it would presumable permit the construction of other more efficient light engines that prevent the spillage.

Mark

This ratio should be calculated using the actual position of the arc to the rear fresnel and the center of the triplet length to the front fresnel.

DJ

My bad. . But the focal lengths of the Fresnel's are what defines where those positions will ultimately be... So there .

Mark

So a longer focal length rear fresnel would result in the ability to use a larger arc? From everything I've read it seems like a 220mm rear fresnel is brighter than a 330mm.. I guess that even though the circle is larger with a longer FL fresnel the bulb's distance from the fresnel still kills the brightness? The larger inner circle would still explain the more evenly lit image that people get with a 330mm rear fresnel, though.

What's the deal with the soft aperture? Is it a characteristic of the lens that's separate from the diameter and focal length?

The 320mm FL standard triplet looks like the most realistic thing for me to use, so should I go with a 330mm front fresnel instead of a 317mm front fresnel? I guess the 220 rear fresnel will give me the brightest image with any of the currently tested/proven/popular lamps.

If someone comes up with a more efficient light engine I don't think it's going to be me so I'm pretty much limited to what's already available.

Again, thanks for the suggestions, clarification, and advice!

But the arc stayed the same size, so the increase in circle size could not overpower the losses of having less light actually impacting the Fresnel.
Exactly . But another difference (and the one everyone talks about) here is that the Fresnel gets more evenly lit the further back you go.
Yes. It is an aperture that varies in size depending on what angle you are looking at the lens from. If you imagine the lens as just a tube with no lenses, then you if you look head on through the tube you see the tube's full hard aperture. But as you tilt the tube, the light gets pinched off by the sides of the tube. The aperture that you can see through gets smaller and smaller until you can see nothing (all you can see is the inside wall of the tube). The width of that visible opening through the tube is the soft aperture. As you can see, the outer edges of the panel would be looking through the tightest angle at the lens. So the light from the edges of the panel must be more finely controlled to make it through the opening. The small circle (soft aperture circle) defines where the light would have needed to have originated back at the bulb to hit that opening.

The angle that the total cuttoff occurs is the Field Of View of the tube (lens).
Yes. Stick to the basic Pro or Standard LL setups. They balance these factors pretty well for the basic light source. We don't yet have a light source that can take advantage of a larger circle.

Eventually I'm sure someone here will build a really nice spotlight that fills the panel perfectly (with little spillage), and keeps the source to a fairly small circle. Then the optics can be designed forward from that knowing what size circle we need. I think just a basic flashlight design would be unreal.

edit: I just realized this conversation should have taken place in the Light Engine Tolerances thread. Doh!
edit by dazzzla: Moved it.

edit Thanks Dazzzla.

Mark

I have gained all of this new knowledge and am still going to end up using the same thing as I was planning on before, but now I know why I'm using it! This thread really sheds some light (pun++) on some of the finer intracasies of how the projector works, and I'm certain that it will be a valuable resource to the less knowledgable.

Still, I've got just one more itty bitty question. ..Should I use a 330mm front fresnel, or a 317mm.. (and here's the big question: why!?

Thanks!

I assume you are using a 15” LCD, a standard triplet , a 20mm gap and a 120" screen. If you are going unsplit then I would be aiming for around 380mm FL front fresnel. But that will probably cost you in the vicinity of $100. For split you’ll need around 340mm FL so the 330mm is the closest. Have a play around with the focal calc and take note of the LCD distance.

DJ

I'll actually be using a 17" LCD, but it will be masked off to 16:9 so it will be ~15". You're right about the standard triplet, but I have no idea about the gap (between fresnels I assume? then yes it will be ~20-25mm). I'll be using split fresnels since the projector will be hanging from the ceiling, and the focal length calculator tells me that I'm going to get an 86" 16:9 screen where the projector will be hanging.

So 330mm is still my best bet? Thanks!

Absolutely fascinating, Mark.

If I built a Total Internal Reflection lightbox with fluorescent bulbs in it and cut a 2cm diameter hole in the box and placed the hole at the appropriate distance from the center of the fresnel, all of the light that exits the hole will contribute to projection?

Is that right?

Tgreenwood

All of the light that exits the hole and impacts the Fresnel could project, yes. But that is only if your projector traces out to a 2cm hard aperture hoop, if you have me there. To say that all of the light will project would require that your design trace to a 2cm soft aperture hoop from the edges of the Fresnel. What this illustrates the clearest is that nothing wider than that 2cm hole could have projected. There would be no point in making the hole any bigger.

Mark

Ok, so i think i understand all this. And from what i understand it seems that the design i have come up with will be unevenly lit. (maby?) I want to use a 10.6" lcd with a 220mm rear fresnel and a 180mm front fresnel and triplet. The triplet is the same size as the LL standard one just with a 180mm focal length. (yes i know the throw will be extremely short). I plan on using a bulb that has a 15mm arc with a precondencer. How would this apply to that design?

Here is the whole method drawn up for your design. I cut some corners in terms of what should be done between the Fresnel Lenses, but it should be pretty close.

Click to view attachment

Any light projecting from the Red arc could project. It represents your hard aperture hoop.

Any light projecting from the Green arc will project. It represents your hard aperture hoop as traced from the edge of the panel.

Any light projecting from outside the Red arc won't project.

Any light projecting from the edge of the Red arc will only project if impacts the center of the panel. None will project if hits the edge of the panel. As you get closer in towards the edge of the green hoop, you can impact further and further towards the edge of the panel.

The 1.5cm arc will fit fine into that 3.8cm soft hoop. Hence there is 1 advantage to moving the triplet closer as you have and using a small panel.

You can see the method for establishing both the hard and soft apertures for the lens with the black lines in the drawing. I guessed that the Standard Triplet is 4cm long. If not, the soft aperture I calculated is going to be wrong. Assume it to be larger the shorter the lens gets.

Mark

Wow, that is a more exact answer than i could have hoped for but now seeing it done like that makes it make a lot more sense to me now. I had thought that i may have made it so my circles for the light to pass through would be small. I guess i was wrong with that. It looks like my design will work beter than i thought.

Here is roughly how the standard Triplet would have traced out:

The soft aperture hoop has now shrunk to 2.9cm from 3.8cm and the hard aperture hoop is 4.2cm from 7.1cm.

Mark

Roughly done, here is the Standard Lens VS the Pro Lens with your panel.

Click to view attachment

The Standard Lens has a 2.9cm soft aperture hoop and a 4.2cm hard aperture hoop.

The Pro Lens has a 2.8cm soft aperture hoop and a 3.3cm hard aperture hoop.

What this tells us is that while the soft aperture hoops are pretty much the same, the hard aperture hoop is about 1cm wider with the Standard Lens setup. This might even suggest that while the edge of the projection should be about equal with both setups, the center may actually be brighter with the Standard Setup with some builds.

Mark

Mark, why 32cm for the std and 65cm for the pro ? Std Lens is 32cm FL, but the pro is only 50cm FL. In actuality the Pro Lens will be greater than 50cm, perhaps even closer to 65cm as shown, but then the standard lens should be shown differently for the comparison ? Just curious if we're comparing 'apples to apples' is all.

gs

What I would like to have included in the model was a standard way to first establish the exact optimal distance between the Second Fresnel and the Triplet. But, to be honest, that is a whole separate model in itself and it seems tricky. I don't think we ever figured that out. Fortunately, I don't think the numbers would change much.

So instead (for now) I just looked at the Second Fresnel focal length (that is where the 65cm comes from). Then I rounded the 31.7cm to 32cm. I just wanted to get a rough idea. I apologize for the roughness of the drawing there, I really only wanted to give a rough example for people to know how to draw their own. But it would be so nice to get that last bit figured out. Yeah, maybe what I should have done for now was look only at the Triplet focal length. You are right, it would have probably been a closer comparison.

Mark

It can be done just requires a couple more steps.
First you use the focal calc to find the LCD distance. Using a 15” LCD, split, a fresnel gap of 15mm and a 120” screen, the LCD distance will be 361mm.
Then you need to calculate the combined FL of the front and back fresnels using this equation: EFL= (F1*F2) / (F1+F2-gap). For a 220mm and a 330mm and a gap of 30mm between fresnels it will be 139.6mmEFL. After you have found the soft aperture size of the triplet (black lines in your diagram) and traced the soft aperture lines back (green lines in your diagram), you need to trace another line (my added purple line) back parallel with the principal axis and then through the EFL to appoint where it intersects your green line. This is the position that the arc will be to create an image at 361mm
Click to view attachment
Mathematically the soft aperture hoop calculates at 29.58mm.Graphically it measured about 27.5mm. My accuracy of the graphical trace wasn’t that great .


BTW, The Pre-condenser Calculator can give the soft aperture size of the triplet. The”Virtual Arc Image Constraints- Max Height” is similar to your soft aperture hoop except it has a pre-con involved.
One of these days I should re-write both of these programs into one.

DJ

That is so awesome . I am just going to take your word on how this one works for now , but it sounds good.

Mark

I was thinking about the original illustration with an LED design. Would it be better to place the LED's along the colminating edge, so that they form a V shape?