Building a small pattern projector

[Sven3376]

Summary: calculation a projection lens system for a pattern projector

Summary: calculation a projection lens system for a pattern projector

Hello,

I want to build a small pattern projector. This projector should project a pattern on a wall, which is 200mm away from the projector. The size of the projected pattern at this distance should be 110 x 110 mm. The dimensions of the projector should be 25 x 25 and max. 50mm long. I have found this page from Edmund optics, where the describe such a system (starts at the middle of the page: Application 3: Building a Projection System) https://www.edmundoptics.com/resources/application-notes/optics/optics-application-examples/
They said, that I need two lenses for the projection lens system and two lenses for the condenser lens system. For the illumination I use a 40W LED with a diameter of 20mm. My magnification M = Image/Object = 110mm/10mm = 11. On this site they calculated the lenses for the projection lens system as follows: F1 = F2 / M (where F2 is the throw distance). So my F1 = 200mm / 11mm =~18mm. So I need two achromatic lenses with a focal length of 18mm. For the condenser system the use this formula: F2 = F1 * M = 18mm * 11mm = 200mm. So I need two PCX lenses with a focal length of 200mm. I´´ am not sure if this calculation is correct. For me, it seems a little bit to easy what EdmundOptics is calculating there? What do the experts say?

best regards,
Sven

 

[berkeman]

Welcome to the PF.

For the illumination I use a 40W LED with a diameter of 20mm.

What is your image? Is it some translucent slide that is illuminated by this LED light source? Are you putting a diffuser between this LED light source and your translucent slide?

Also, the Edmund Scientific article didn't seem to focus on projector optics, but maybe I misread it.

What distortion specs do you need to meet for this school project, and how can you check your design for the distortions? Are you allowed to use lens design software as part of this project?

 

[BvU]

Not an expert, but obviously you are severely constrained by the 50 mm maximum length of your apparatus. You have 39 mm minus total glass thickness minus LED thickness for your condensor object distance + (part of) image distance.

Is the 10 mm object size a given ? And the 20 mm LED ?
Do you know the angular distribution of the LED light ?

You don't mention lens diameters but do you realize an 18 mm focal length lens is very small and pretty thick ?

I seem to remember you basically want to have an image of the light source at or near the position of the projection lens to maximize brightness. With image size $\approx$ lens diameter. But that's for slide projectors where filament size usually $\ll$ slide size. Like here

How it works for a 20 mm extended light source and a 10 mm object is unclear to me.

Whatever, you can't do much useful with 200 mm focal length lenses in a 50 mm space...

@berkeman was a lot faster -- I google very slowly

 

[sophiecentaur]

Are you putting a diffuser between this LED light source and your translucent slide?

Projection systems have had a lot of design work on them because cinemas need the brightest possible image on the screen.
As I remember, a diffuser would just lose light. To minimise loss, the condenser system is designed to project the source image (in the past, this would have been a rectangular array of filaments) actually on the projection lens so a maximum amount of light gets through the lens and the slide. The slide is placed at the focal plane of the condenser system which will be the Fourier Transform of the bulb filament (? I think that's right). For each point source of light, the Fourier transform gives a uniform illumination of the slide - good value. The condenser pair are pretty cheap and cheerful because the usual requirements for lenses are pretty lax - no one is looking at image quality of the illumination. The projection lens needs the best design affordable / achievable.
@BvU The OP needs to do a fair bit of homework before actually starting to build anything. You've pointed out a number of difficulties (if the projected image actually needs to be as bright as possible). To 'just get it to work', life could be a lot easier.

 

[Sven3376]

Hello,
thank you for your answers. I try to answer everything.The slide is a glass slide where a pattern is printed on, so that the LED light source can shine trough it. I want to use a condenser system with no diffuser between the LED and the glass slide. I hope that´s enaugh?hm..I thought, that they where calculating lenses for a projection system at the end of the EO site.The pattern can have distortions (I don´t know how to quantify this?) and I´m allowed to use any software and help :-)

Is the 10 mm object size a given ? And the 20 mm LED ?
Do you know the angular distribution of the LED light ?

The pattern size is given and it is 10mm. The 20mm lens is not given, but it was the most powerful one, that I have found. I can also use a LED with a diameter of 10mm, but then the LED does not have such a high power and I need a lot of light.

ou don't mention lens diameters but do you realize an 18 mm focal length lens is very small and pretty thick ?

Lens diameter is limited to 25mm max. EO has lenses with a focal length of 20mm and a diameter of 20mm.

How it works for a 20 mm extended light source and a 10 mm object is unclear to me.

I can also use a smaller LED

Whatever, you can't do much useful with 200 mm focal length lenses in a 50 mm space...

yes right, but the 200mm fl lenses were the results using the equations from the EO-site. Maybe I can use lenses with smaller focal lengths?