Lenses

From Lumenlab

by SupraGuy

Essentially, lenses bend light. When light enters the lens at an angle, it is bent at a refraction angle determined by the optical properties of the lens material, as compared to the material that they left (Typically air.) I’d suggest taking a look at HowStuffWorks.com “How fresnel lenses work” as some basic information, as well. There are also links there to a lot of other interesting things having to do with lenses and projection.

First off, the general drawing from the Guide gives a good idea of light transmission though the projector, but it’s often misinterpreted as being the light path which gets projected. This is simply not the case. Brain’s drawing is not one of the projection, but simply of the usable and needed light path through the projector in order to hit the projection lens. (Fig. 1)

We’ll start with the collimator fresnel. What this lens does is in the diagram, it takes the diverging light rays and bends them to make a set of parallel rays. It does NOT focus the light rays, and in fact, as we’ll see later, at this distance, it is impossible for it to focus the light from the lamp on anything. In order for it to do so, the lamp would have to be at a distance greater than the focal length of the lens.

The field fresnel could, in fact focus the light, and if you were to remove the triplet and place a “screen” at an appropriate distance from the field fresnel, you would get a focused image of the lamp. It would not be a high quality focused image of the lamp, but it would be there. It is important to distinguish that neither of the fresnels actually focus on the LCD, they are merely there to direct the light from the lamp through the triplet. It is entirely possible to make a projector without these fresnels at all, however, it would far less efficient, requiring much greater light input and delivering much lower output.

So, let’s get to the interesting lens… The triplet.

This is the lens that actually focuses on the LCD. In theory for a monochrome image, there would be no advantage to a triplet over a single lens. This is because lenses treat different colours differently. Red light has less energy, and is deflected at a different angle than the higher energy blue light. This is why crystals produce rainbows – the same thing is actually happening in your projection lens, but the triplets are aligned in such a way as to re-integrate the light at the output, while still having the desired focusing effect.

For purposes of this write-up, we’ll treat the triplet as a “perfect” single convex lens.

The focal distance of a convex lens is defined as the point where parallel light entering the lens will converge to a point. While this exact distance is useful for starting fires with a magnifying lens, it’s actually not much good in a projector. The following figure represents an LCD at the focal distance of the lens. You can see that what you get projected onto the screen isn’t the 3 distinct points on the LCD, but a big mess. In fact, what you may notice is that the individual points are each the same size as the lens. This is “infinite focus” Where a screen which is far enough away that this limited resolution is not a problem. (Fig. 2)

Fig 2

So if we look at an example of the same image focused, the image source (LCD in our case) is further than the focal distance of the lens. You will see that we have distinct points back on our screen, in a scaled reversal of the points on the LCD. The light represented on the left side of the lens is only the light that we’re interested in. There is generally going to be more of it than what I’ve shown, but only the light that hits the lens gets projected. On the right side of the lens, however, is the most light that there can be. (Fig. 3)

Fig 3

Now we can step back to the field fresnel. This lens alters the light path somewhat, but does not actually produce a focus. The reason for this is that the lens is far too close to the LCD to do what the projection triplet does. Remember that we’re only interested in the light that hits the triplet. Due to the nature of what the collimator fresnel does, the majority of the light leaving the LCD is not headed for the triplet, but is instead going straight forward, in parallel beams. Naturally the LCD scatters this a bit. The field fresnel redirects that light so that it hits the LCD. I’ll say it again, it does not focus it. The following figure shows what generally happens to the light leaving the LCD, passing through the fresnel (Not to be confused with the previous marker for focal distance) and hitting the projection lens. You will see that at the projection lens what you get is the sum of ALL of the light passing through the LCD. You sill also see that from the point of view of the projection lens, the LCD screen would be magnified, appearing close than it actually is. This modifies the effective focal length of the projection triplet, requiring a greater distance from the combination to generate an effective focus. This is also how the field fresnel assists with keystone correction, by being further from the LCD, the magnification effect becomes greater. You will see that as the light progresses, it is still diverging from it's point source, and as such it will never be able to truely come to a focus. As mentioned before this is because the LCD is too close to the lens relative to its focal distance.(Fig 4.)