DIY Projection Lens Triplet - diyAudio

long throw projector

Dee:

First of all, I would not recommend a 122" image. I think that will be too large to view comfortably. (Your neck gets tired after a while from moving your head back and forth ???? ) But I will show you the math, so you can work it out if you really do want 122".

Here is the optical geometry for a 100" image, assuming a 16' throw distance and a 15" LCD:

M is magnification
A is the LCD to projection lens distance
B is the projection lens to screen distance
FL is the focal length of the projection lens

M = 100" / 15" = 6.67

FL = B / (M + 1) = 16' / (6.67 + 1) = 2.086' = 636 mm

A = B / M = 16' / 6.67 = 2.40' = 731 mm

So you would need a 636 mm fl projection lens. You can try making that from a pair of positive meniscus lenses using this:

EFL is the effective focal length of a multi-element projection lens
FL1 is the focal length of the first simple lens
FL2 is the focal length of the second simple lens
D is the distance between the lenses

FL = (FL1 * FL2) / (FL1 + FL2 - D)

If you space them too far apart, then you limit the field angle too much. Eyeglass lens blanks come in 1/4 Diopter increments.

Diopters = / focal length in mm

So you can get +1.0 Diopter ( mm fl) and +0.75 Diopter ( mm fl) lenses. The large steps make it difficult to make specific long-throw projection lenses from eyeglass blanks. So let's see what happens with a mm and a mm lens with 30 mm of space:

EFL = ( * ) / ( + - 30) = 578.81 mm

Feeding this back into your room and LCD size constants:

M = (B - FL) / FL = 7.43
Image size = 7.43 * 15" = 111"

Now we can recalculate A for this lens:

A = B / M = 16' / 7.43 = 2.15' = 656 mm

So that tells us you need about 656 mm from the LCD to the projection lens. If you use a split design, then you would put a (656 - 20) = 636 mm fl fresnel 20 mm after the LCD. If you use a non-split design, then you would put a (656 + 20) = 676 mm fl fresnel 20 mm before the LCD. These long throw fresnels may be very difficult to find! Lumenlab.com used to sell a "790 mm" fl fresnel (that I measured to actually be about 770 mm fl). You could ask them if they have any left. They were changing to a shorter focal length (650 mm?, 600 mm?), for use with a 450 mm fl triplet, so they may have a "790" they could sell you. Even if they don't, you could still use a 650 or 600 mm fl fresnel by adjusting the distance between the lamp arc and your condensor fresnel.

So the short answer is: Keep the 220 mm fl fresnel. Find a 770 mm field fresnel. Buy +1.0 and +0.75 Diopter eyeglass lenses and put them in a tube. The Rolyn lenses that tgreenwood mentioned only go down to +1.0 D in the acrylic. You will have to buy a glass +0.75 D. This will give you an image that is good enough for watching video, but a bit blurry around the edges for running windows. If you want a sharp image from corner to corver, you will need to find a triplet or tessar lens designed for somewhere in the 550 to 650 mm fl range.

This is a continuation from the previous tutorial - achromatic doublet lenses.

Link to CLZ

In , a new type of triplet lens for photographic applications was invented by the
English designer H. Dennis Taylor. He realized that the power of two lenses in contact of equal, but opposite, power is zero, as is its Petzval sum.

As the lenses are separated, the system power becomes positive since the negative lens contributes less power. The Petzval sum remains zero, since it does not depend upon the marginal ray height. In order to overcome the large aberrations of such a configuration, Taylor split the positive lens into two positive lenses and placed one on each side of the negative lens. A stop is often located between the negative and rear-positive lenses.

Figure 22 illustrates a typical triplet lens. The triplet can be used at reasonably large apertures (\(\gt{F/4}\)) and moderately large fields of view (\(\gt\pm25°\)).

The triplet has eight degrees of freedom which are the three powers, two airspaces, and three lens bendings. The lens powers and airspaces are used to control the axial and lateral chromatic aberrations, the Petzval sum, the focal length, and the ratio of the airspaces.

Spherical aberration, coma, and astigmatism are corrected by the lens bendings. Distortion is usually controlled by the airspace ratio or the choice of glasses. Consequently, the triplet has exactly the number of degrees of freedom to allow correction of the basic aberrations and maintain the focal length.

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The design of a triplet is somewhat difficult since a change of any surface affects every aberration. The choice of glass is important and impacts the relative aperture, field of view, and overall length. For example, a large \(\Delta{V}\) produces a long system.

It should be noted that a triplet corrected for third-order aberrations by using the degrees of freedom almost always leads to a lens with poor performance. A designer normally leaves a certain amount of residual third-order aberrations to balance the higher-order terms.

A few years later, Paul Rudolph of Zeiss developed the Tessar, which resembles the triplet, with the rear lens replaced by an achromatic doublet. The Tessar shown in Fig. 23 was an evolution of Rudolph’s anastigmats which were achromatic lenses located about a central stop.

The advantage of the achromatic rear component is that it allows reduction of the zonal spherical aberration and the oblique spherical aberration, and reduces the separation of the astigmatic foci at other than the design maximum field angle.

Performance of the Tessar is quite good and has generally larger relative apertures at equivalent field angles than the triplet. A variety of lenses were derived from the triplet and the Tessar in which the component lenses were made into doublets or cemented triplets.

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