Here is some theory behind our DIY projectors that members might find useful. I don’t claim to be any sort of expert, this is just a collection of stuff that I’ve read, some of it I’ve tested and some that I’ve reasoned. It’s not for the complete noob so some basics are needed to understand it. It is probably already on this site somewhere but I just wanted to put it into a brief summery. I hope it helps.

Although there appears to be only one optical system in a projector, it can be split into two more easily described systems, Imaging and Non-imaging.
Non-imaging optics is a name given to optics that doesn’t deal directly with the image. These are things like the fresnel lens, reflectors, lamp arc, pre-condensers etc. They are only concerned with what happens to the light that they interact with, how much light, light distribution, beam angles, basically controlling the light path.

Imaging optics, such as the triplet, are more concerned with the quality of the image, image size, image aberrations etc. With DIY projectors we have little control over the image optics. The triplet designer generally decides them for us but it is still helpful to understand them. Non-imaging optics is where we have a greater choice

Because there is only one light path for the light to travel, that is from the lamp through the optics and LCD to the screen, the two principals are hard to separate. One way to think of it is if you set up just the LCD and triplet to the correct distances (imaging optics). Now use a powerful torch at different locations behind the LCD to direct the light though to the triplet (non-imaging optics), you could get all of the LCD to project an image, just not all at once. The point here is that the non-imaging optics can be varied to some degree without affecting the imaging optics. This pic shows how the non-imaging optics can be varied.

The way we set up our non-imaging optics is called finite to finite optics. This is because the light starts out from a small source (finite) that diverges, it is then collimated and then converges to a point again. In a commercial projector the non-imaging optics could be described as finite to infinite. There is no need to converge the light because it is small enough to fit through the objective lens.
Our goal is to control the light in such a way as it will resemble the ideal pic as close as possible.

Point Source:
If it were possible to use a point source then after the light passed though the optics it would diverge correctly to a point. This is not really possible because of the arc length. If the same FL was to be used for both Fresnels then after the light from the arc has passed thought the optics to the other side it would diverge to the same size as the arc, this is called the arc image. So for an arc that is 25mm long, it would have an arc image that is 25mm long

For this reason we need to use a relatively large triplet (80mm) with a good field of view. A commercial projector on the other hand can use a much smaller objective lens that has a very narrow field of view. The problem gets worse as the FL of the front fresnel is increased. Take the standard OHP fresnel pair for example, it has 330/220mm FL combination. This creates a arc image that is 37.5mm in length. The larger the FL becomes compared to the rear, the larger the arc image will be.

Light Distribution:
The next three explanations are to do with dim corners and they all contribute to dim corners with varying degrees.
Inverse Square Law: When light from a point source falls onto a flat surface, such as the fresnel, it won’t be evenly distributed. The smaller the angle of incidence the less light there will be on that area. You could increase the rear fresnel FL so that there is a smaller difference between the centre of the image to the outer edges it would be at the expense of the total amount of light that passes though the image.

Reflections: When light strikes a transparent surface such as the back of a lens not all of the light will pass through, it will reflect some. The larger the angle of incidence the greater this reflection will be.

Fresnel rings: The problem with fresnels is the way that the lens is flattened. The drafts, which are the concentric cuts that make the fresnel, are deepest at the outer edges of the lens and cause shadows. In an ideal set-up, point source at the FL, the drafts would be very visible but because we use an arc this problem is blurred. If the lamp is moved from the FL the shadows will become more of a problem. This is why a fresnel should be used close to its designed specification.

Spherical aberration
A spherical lens suffers from what is known as spherical aberration. It is caused because the outer edges of a lens refract the light rays to a point closer than the FL. Here is a ray trace showing what happens when collimated light passes through a lens.
As you can see the outer most rays fall somewhat short of the FL. Ideally they should all focus to one point.

Now here’s what happens when light passes through the lens from a point source. This time the outer rays are diverging while the inner rays are close to being parallel. Ideally they all should be parallel.

You might think that it is a simple matter of moving the point source closer to the lens to make it parallel. Although the outer rays are parallel the inner rays are now diverging.

The problem only gets worse when another spherical lens is added into the optical path to complete the finite to finite optical methodology. the first lens adds its spherical aberration and then the second lens adds even more.

Aspheric Lens
There is a solution and that is to use aspherical lenses. An aspherical lens is really two spherical surfaces combined into one. If you look at this pic it shows the two lens surfaces overlayed and each have their own FL. When they are combined the spherical aberration can be corrected.
The fresnel lenses that are designed for non-imaging are generally aspherical fresnels and as I’ve stated above should only be used close to their FL. If you move the arc to far from the FL or off axis from the centre you will cancel its correction.

The main idea for non-imaging optics is to find the best solution of components to allow the greatest amount of light to be collected and directed to the triplet. It should also be well distributed. That’s enough babbling for the moment I hope that this helps someone.

DJ

.... cooooll dazzzlaaa .....

well put man! ...are you a physicist/optometrist ?

Couldn’t stay at school for that long.
Thanks for the complement.

DJ

Dazzzla,

Speaking of nonimaging optics - a hyperboloid "trumpet" may be practical for max light gathering. I'm referencing a solar concentrator for this one. All light entering a hyperboloid trumpet fromo any direction will "bounce it's way down to the bottom after X reflections. If this could accumulate off axis light with a concentration lens at the end of the trumpet to focus this light, hmmmmm...

Going to have to think on this one more before posting further info.

John

Excellent work Dazzla! This should be added to LL's WIKI. I'm sure it'll help a lot of people out.

jerseyjohn
Although a hyperboloid would collect a large amount of light, I’m not sure wether it would rearrange the rays to in any useful order but I could be wrong.

Hyper Smiley
I thought about putting it in the wiki but I think there needs to be some basic optics theory in there first to understand it. As well as I don’t know how to add to the wiki.

DJ

Fixed a couple of stuff ups. Virtual arc image should have been called arc image (doh)

DJ

Thanks Dazzzla You always do such great work for once the drawings show the arc imageat both ends You should be pinned.

Thank you for the info! I don't know if there's anything I can do with it right now, but it's in the memory banks for later...

very well described DAZ. I would love If somebody would have explained that way to me

Thanks. I was intending to put this info into the wiki but never got around to it. I’m slack some times

DJ

DAZZ: I can rework this and stick it into the wiki sometime in the next couple of weeks if ya want me to.

Go for it.

DJ

Done.

Please check it fer me. --> Imaging and Non-imaging Optics

I linked it as a one-level-deeper page from the standard guide instead of as a separate page of its own so folks have the option of skippin' it. Feel free to change that, of course, as always.

I wuz too lazy to remove the trailing whitespace in some of the images. Maybe later.

I also find it cumbersome the way I have to insert the images. Maybe I'm just being stoopid. I see there were plans to allow FTP access for uploading but I assume that never came to pass?