6x9 or degree

[gafftapegreenia]

Alright, I was trying to stay out of this one, but, well, here goes.

As a base, let me establish that I am talking about the 360Q and all of its copies/brothers/relatives in the world.

As we all know, an ellipsoidal reflector has two focal points. The first focal point, as we will call it, is located inside of the reflector. It is at this focal point that the filament of the lamp of the ellipsoidal is ideally located, so that the filament is best positioned for the reflector to most efficiently and evenly capture the light. Ideally, this would be a point source, but because there is no such thing as ideal point source in theatrical lighting, an ellipsoidal reflector is slightly modified to account for the linear filament. This modification that allows better performance does not change the principal of how an ERS works.

The reflector never changes. In the 360Q series, all reflectors are of the same shape and focal length.

The second focal point is located outside of the reflector. In an ellipsoidal, this focal point will be just past the shutters/gobo holder. If the focal point were infact at the shutters, there would be little to actually shutter cut and the shutters would essentially be useless. Same goes for the gobo. If the focal point was actually on the gobo, little of the image would be captured. By having the focal point just past the shutters/gobo, the majority of light coming through the opening is essentially the same diameter as the opening itself, thus it can be effectively chopped and gobo'd. (I made a word) Note I say majority. In a perfect world with a point source, all the light would be focused. However, because of the imperfect filament, there is stray light that is captured. This is the same stray light that makes gobos fuzzy, even in a perfectly centered, hard focused ERS.

Now, if you ever take apart various degree 360Q's, you will notice that the lens trains are in fact all the same length. This is one part made for all the models. The differences are that the lenses put into this lens train by Altman are of difference focal lengths, and the longer body of a higher 6-x-whatever places the lens train farther from the second focal point of the ellipsoidal reflector. Take, for example, a 6x9. It has a 6" diameter lens with a focal length of 9". When in hard focus, the first lens in the lens train will have its focal point, which is 9" away, at the second focal point of the ellipsoidal reflector. Since the focal point of these two items is in the same location, all the light that strikes the first lens in the train will leave that lens as parallel rays. The second lens is then positioned to take those parallel rays and focus them back down. The focal point of the second lens is 9" in front of the fixture. The rays of light converge hear, and then spread as they make their way to the stage. As you move on to 6x12's, 16's and 22's, the fixture becomes longer because, since the lenses used have longer focal lengths, they must be farther away from the focal point of the ellipsoidal reflector in order to focus correctly.

The relationship of the two plano-convex lenses is a constant. It is the relationship of the focal point of the first plano convex lens to the focal point of the ellipsoidal reflector that is user selectable.


Now, what ETC did, and what was the genius part, is that they decided they wanted to use the same body length for all their fixtures. So, using math and engineering brilliance, they departed from the double plano convex system. Each degree of Source 4 uses a specially designed set of lenses. Some have one lens, others have two, some use biconvex lenses, which are rounded on both sides. All of this allows different lens combinations to produce difference beam spreads, while keeping all instruments of uniform length. By changing the lenses themselves, ETC was able top make lens trains interchangeable, thereby revolutionizing the industry.

So, that is my understanding.

Charc, you second graphic is showing an ERS that is not in hard focus. The lens train on that ERS would be all the way in, thus spreading the rays as they leave the first plano convex lens, and giving a soft beam/image.

 

[Serendipity]

The second focal point is located outside of the reflector. In an ellipsoidal, this focal point will be just past the shutters/gobo holder. If the focal point were infact at the shutters, there would be little to actually shutter cut and the shutters would essentially be useless. Same goes for the gobo. If the focal point was actually on the gobo, little of the image would be captured. By having the focal point just past the shutters/gobo, the majority of light coming through the opening is essentially the same diameter as the opening itself, thus it can be effectively chopped and gobo'd. (I made a word) Note I say majority. In a perfect world with a point source, all the light would be focused. However, because of the imperfect filament, there is stray light that is captured. This is the same stray light that makes gobos fuzzy, even in a perfectly centered, hard focused ERS.

Now, if you ever take apart various degree 360Q's, you will notice that the lens trains are in fact all the same length. This is one part made for all the models. The differences are that the lenses put into this lens train by Altman are of difference focal lengths, and the longer body of a higher 6-x-whatever places the lens train farther from the second focal point of the ellipsoidal reflector. Take, for example, a 6x9. It has a 6" diameter lens with a focal length of 9". When in hard focus, the first lens in the lens train will have its focal point, which is 9" away, at the second focal point of the ellipsoidal reflector. Since the focal point of these two items is in the same location, all the light that strikes the first lens in the train will leave that lens as parallel rays. The second lens is then positioned to take those parallel rays and focus them back down. The focal point of the second lens is 9" in front of the fixture. The rays of light converge hear, and then spread as they make their way to the stage. As you move on to 6x12's, 16's and 22's, the fixture becomes longer because, since the lenses used have longer focal lengths, they must be farther away from the focal point of the ellipsoidal reflector in order to focus correctly.

1. Thanks for the amazing post, Greenia.
2. Because the second focal point is further away in smaller beam spread fixtures, would it have an affect on the less-than-perfect filament's extraneous light, making it more difficult to create sharper-edged patterns? Because in S4s the location of the shutters/gobo does not change, even if using the behemoth 5°s..? Or am I creating some sort of fallacy in my head?

Thanks!

 

[cdub260]

I'm essentially disregarding what you're writing, and attempting to explain my perceived understanding of ERSs, but am open to correction.

Looking back at the previous diagram, the Primary Focal Point is the Filament, and that point is static for the 405 through 490, simply because all of those units use the same lamp, same housing, and same reflector. That makes their relationship to each other constant. If you were to remove the barrel from both your hypothetical 405, and 490, then the output of light from both bodies should be the same, no?

No when you put in the barrel, you're also putting in the lens, or lenses, whatever the case may be for whichever barrel you're using, you introduce a new factor into the path of the light. These optics direct the light to the Secondary Focal Point, but are not themselves the Secondary Focal Point.

The Primary focal point has to be the lamp (filament), because that's what the source is. The secondary focal point is where the light, once again, (theoretically) comes back to one point, before spreading out again. The focal length would be the distance between the foci, right?

Here is another diagram:

As I understand it in the 6xwhatever notation, a 6x9 was an elipsoidal reflector spotlight with 6 inch lenses that had the focal point of the beam 9 inches out from the front of the light. A 6x12 would have it's focal point 12 inches from the end of the light, etc.

As an experiment, you might try putting on a thick pair of gloves and holding your hand 16 inches from the front of a 6x16 or 19 degree. I did this, probably 15 or so years ago, and smoked a ratty old pair of gloves. Just don't try putting your bare hand in the beam.

Thanks charcoaldabs for this wonderful diagram.

In my original post I screwed up my terminology. Bear in mind its been 18 years since I had my lesson on how lekos work, and haven't thought about it much since. What I was referring to as being "16 inches from the front of a 16 degree" was the point where the beam crosses itself.

Feel free to correct me if I'm wrong here.

 

[LightStud]

Thanks charcoaldabs for this wonderful diagram. ...

Wonderful? Perhaps. Inaccurate? Absolutely.

N.B., Speaking mathematically, ellipsoidal shapes do not have focal points. Focal points are a component of a lens', or lens system's, definition. Conical sections have one focus or, in the case of an ellipse, two foci.

In the diagram, only the two outer light rays are shown leaving the secondary focus of the reflector. One assumes the others have been omitted for clarity, a marginally acceptable practice. Had some others been included, the following error might have been avoided.
Can anyone explain how a lens system can possibly take a single light ray and bend it two different places, one veering off away from the longitudinal axis and the other bending toward it?

 

[SteveB]

By changing the lenses themselves, ETC was able top make lens trains interchangeable, thereby revolutionizing the industry.

Excellant post, BTW.

And FWIW, Century Lighting had interchangable lens tubes on their LekoLite series in the 60's ?, or whenever the old grey radial ellipsoidals were introduced. The 4.5x6, 6x9 and 6x12 lens tubes were interchangable between bodies. Colortran, Kliegl, ADB/CCT among others had this feature before the S4 ellipsoidal was introduced in the early 90's. For whatever reason - cost ?, not wanting a different standard ?, the biggie rental shops stuck with the 360 and 360Q until the S4.

So this part wasn't really revolutionary, even though I agree with the rest.

Steve B.

 

[church]

Actually the mathematical definition of an ellipse is:

an ellipse is the path traced out by a point whose distance from a fixed point, called the focus, maintains a constant ratio less than one with its distance from a straight line not passing through the focus put anothr way: an ellipse is a locus of points in a plane such that the sum of the distances to two fixed points is a constant. The two fixed points are called foci (singular- focus). An easy way to draw an ellipse to illustrate this is to make a loop of string hammer two nails into a piece of wood. Loop the string around the nails - hint this only works if the loop of string is bigger than the distance between the nails. Then place a pencil inside the loop and move the pencil until the loop is tight. then move the pencil always keeping it tight to the string as if you are trying to draw a circle - you will end up with an ellipse. the two nails are your focal point.

In an ellipsoidal you want the filament of the lamp to be as close to a spot as possible located at one locus. Because light travels in straight lines (at least in the wave nature of light - lets forget photonic behaviour in this instance) the light waves incident on the reflector are reflected at the same angle angle as they are incident to the reflector. This means if the lamp filament was a perfect spot source at the first locus or focus of the ellipse then all the light would also pass through the second focus and into the optics.

You could build an ideal spotlight if you could get perfect bits.

This is why lower voltage fixtures tend to be more efficient because you can make the filament smaller so it becomes closer to the ideal condition. This is why 240v lamps are not as efficient as 120V lamps and why 24V lamps are better still. So if you can improve the reflection coefficient of the reflector you will also maximise the light coming out.

Because you can't make a perfect lamp, reflector or lens we end up with less than perfect fixtures and the debate on which is best and with what combination of lamps. Note dust changes the reflection coefficient of the lenses and reflectors - this is why dirty fixtures give poor light output.


Because you can't get perfect bits to build a fixture the goal is to design one that allows for the imperfections in the design and maximises the performance hence the HPL lamp optimised to the reflector. This can be done with the analysis and simulation tools available to today's engineers but was beyond the reach of engineers in the 80s.



Other applications of ellipses inlude planet orbits, gears etc.