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 Calculating optics for projection onto mirror dome 
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Binocular Vision CONFIRMED!
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I am investigating the possibility of making a display for a museum. The goal is to project onto a partial dome, with perhaps 120 to 180 degrees of coverage.

While fish-eye projection lenses are available, they are extremely expensive. So, projecting onto $40 dome security mirror is much preferred, because such a system is a fraction of the cost. What I am uncertain of, is the focus range needed for the projector.

Paul Bourke's web site has a lot of information, including a statement,"For a 60cm spherical mirror the projector needs to be able to focus to an image that is between 40 and 50cm wide." http://paulbourke.net/dome/faq.html

So, apparently the projector must focus onto the mirror itself. I don't know how to calculate how lens systems work. I would think that focusing on the mirror would result in the image not being focused on the projection surface. I would also expect that the mirror, since it causes light to diverge, would be functioning like a convex lens. Surely this has some effect on the final focus on the projection surface.

In my experimentation with a small projector that I have, adding a magnifying lens by just taping it onto the outside surface of the projector does successfully permit the projector to focus closer. Though, I suspect that this introduces some chromatic aberration, at the weak strength of the lens I tried, it wasn't noticeable.

Can anyone here advise me?

-Joe


Fri Mar 08, 2019 8:46 am
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Diamond Eyed Freakazoid!
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Hi, I don't know if I'm any help but did you think about warping software?
http://www.warpalizer.com/en/sim.html

Or similar, I'm not sure how much it costs and there might be a open source one
https://www.google.com/search?rlz=1C1CH ... C7Wgyq9GrU

https://forums.x-plane.org/index.php?/f ... rojectors/

Theres some links to some setups and searches. Is'nt it too complicated to use a mirror?

Open source warping sofware : https://www.google.com/search?rlz=1C1CH ... VQmwDVhKhk

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Fri Mar 08, 2019 12:53 pm
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Binocular Vision CONFIRMED!
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I was aware that the image will need to be warped. This is because the projector and mirror will not be in the center of the screen. My question, at this point, is just about the focus. I know that projectors typically have a range over which they can be focused. Normally, I suspect that only the near focus is a limitation.

The idea of a projector and a domed mirror has been around for a long time. In fact, there are some desktop versions. Since many people have access to projectors, I am surprised it is not used more often. And even making a diy inflatable dome is not that hard. But, I suspect that the availability of useful HMDs has significantly cut back on interest for projection for the hobbyist. But, for a public display, a dome arrangement is certainly preferable.

I suppose even projection for public displays is going to eventually become obsolete. Flexible OLED displays, on a large scale, can be made into panoramic images, and have wonderful dark levels, even in a fairly bright environment.

-Joe


Fri Mar 08, 2019 3:27 pm
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Diamond Eyed Freakazoid!
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Hi, so you need to know what type of lenses on a projector to get.

https://www.projectorcentral.com/cc990212.htm /here is some info about lenses

There is this projector: https://business-display.benq.com/en/fi ... u9730.html
https://business-display.benq.eu/es/fin ... 1552082206

Ultra-low projection factor LS1ST4: 0.377
Fixed width LS1ST3: 0.76
Zoom ultra-wide LS1ST2: 0.75 ~ 0.93
Zoom wide LS1ST1: 1.25 ~ 1.79
Standard LS1SD: 1.73 ~ 2.27
Semi-long LS1LT1: 2 , 22 ~ 3.67
Long Zoom1 LS1LT2: 3.58 ~ 5.38
Long Zoom2 LS1LT3: 5.31 ~ 8.26
Zoom index Ultra-low projection factor LS1ST4: Fixed Fixed
width LS1ST3: Fixed
Ultra-wide zoom LS1ST2: 1.25x
Wide zoom LS1ST1: 1.41x
Standard LS1SD: 1.3x
Semi-long LS1LT1:
1.65x Long zoom1 LS1LT2: 1.5x
Long zoom2 LS1LT3: 1 55x
Lens control 8 lenses (motorized zoom and focus)
Shifting the objective Vertical: 0 ~ 50%
Horizontal: -10% ~ 10%, standard lens
Trapezoidal correction Vertical: ± 30 degrees
Projection size 80 "~ 500", standard lens

I read this page : http://paulbourke.net/dome/faq.html

They list the projectors to use, But I am guess you need to have the projector mounted a ways back behind the display, you may need a zoom lens. I would contact the projector company and ask them about details before you purchase the projector you need. Maybe I don't know exactly what the specifics are but I would talk to the company and ask " whats the smallest screen size with clear focus on this projector without a zoom lens".

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Fri Mar 08, 2019 4:07 pm
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Binocular Vision CONFIRMED!
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Dom, I appreciate your effort to help me. You are doing a lot of work. However, I think you are missing the main point of my question. Once a projector's light hits a convex mirror, I suspect it will affect the focus of the image on the projection surface. It should shift the focus range in some way. That is what I am seeking to find out.

Note that I can calculate the angle that the beam disperses. The projection image, at the point where it hits the mirror, will be reflected in a direction that is mirrored to a line that is created by drawing a line from the center of the sphere to the point where that light be is hitting the mirror.

-Joe


Sat Mar 09, 2019 7:35 am
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Hey sorry about that, I thought that never matter that much cause paul already tested that and it worked with the same mirror he had.

Heres some info about convex mirrors: http://farside.ph.utexas.edu/teaching/3 ... de138.html
https://en.wikipedia.org/wiki/Curved_mirror

From my understanding, I thought mirrors displayed the exact same image only the convex mirror will be warped. There might be a little focus needed.

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Sat Mar 09, 2019 1:14 pm
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Joined: Fri Mar 08, 2019 6:05 am
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cadcoke5 wrote:
I am investigating the possibility of making a display for a museum. The goal is to project onto a partial dome, with perhaps 120 to 180 degrees of coverage.

While fish-eye projection lenses are available, they are extremely expensive. So, projecting onto $40 dome security mirror is much preferred, because such a system is a fraction of the cost. What I am uncertain of, is the focus range needed for the projector.

Paul Bourke's web site has a lot of information, including a statement,"For a 60cm spherical mirror the projector needs to be able to focus to an image that is between 40 and 50cm wide." http://paulbourke.net/dome/faq.html

So, apparently the projector must focus onto the mirror itself. I don't know how to calculate how lens systems work. I would think that focusing on the mirror would result in the image not being focused on the projection surface. I would also expect that the mirror, since it causes light to diverge, would be functioning like a convex lens. Surely this has some effect on the final focus on the projection surface.

In my experimentation with a small projector that I have, adding a magnifying lens by just taping it onto the outside surface of the projector does successfully permit the projector to focus closer. Though, I suspect that this introduces some chromatic aberration, at the weak strength of the lens I tried, it wasn't noticeable.

Can anyone here advise me?

-Joe


Hi Joe,

You must also consider the projector's distance when setting it up. I read an article from a good site. You can check it here: https://www.outdoormoviehq.com/ultimate ... -distance/. Distance is really important. This is the first step you must apply. Just let me know what you think of this. Also, can you elaborate more how you will install the projector and what projector are you using? :)


Mon Mar 18, 2019 2:58 am
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Binocular Vision CONFIRMED!
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Thank you for the reply, but I am already aware of how to do the calculations with a regular projector set-up. There is even a great web page that does a lot of the work for you. Just enter the model, and it already knows the range of the throw ratio. https://www.projectorcentral.com/projec ... or-pro.cfm

The spherical mirror complicates things. I already know how to calculate the spread of the image. The beam simply bounces off of the mirror in a way that is mirrored from an imaginary line drawn from the point where it hits the mirror, to the center of the spherical mirror. But, I think it should affect how it can focus. I am guessing that it is like adding a magnifying lens in front of the projector's lens. In my experimentation, adding a magnifying lens will allow the projector to focus closer to the projector.

-Joe


Mon Mar 18, 2019 10:18 am
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One Eyed Hopeful

Joined: Fri Mar 08, 2019 6:05 am
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cadcoke5 wrote:
Thank you for the reply, but I am already aware of how to do the calculations with a regular projector set-up. There is even a great web page that does a lot of the work for you. Just enter the model, and it already knows the range of the throw ratio. https://www.projectorcentral.com/projec ... or-pro.cfm

The spherical mirror complicates things. I already know how to calculate the spread of the image. The beam simply bounces off of the mirror in a way that is mirrored from an imaginary line drawn from the point where it hits the mirror, to the center of the spherical mirror. But, I think it should affect how it can focus. I am guessing that it is like adding a magnifying lens in front of the projector's lens. In my experimentation, adding a magnifying lens will allow the projector to focus closer to the projector.

-Joe


Nice to know Joe! When you're all up, just let me know if it worked. I'm excited to see your work. Kindly send me a photo/image when it's done. Cheers and good luck!:)


Wed Mar 20, 2019 12:39 am
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