Optics: infinite light source illusion question - can you help?

[simonlhill]

TL;DR Summary

How can you use a series of mirrors/lenses/prisms/projector/etc to achieve a point of light that appears to be at a near-infinite distance away?

Hi. I’m trying to solve an optics problem and really struggling. The problem is best described as follows…

Imagine you have a section of a wall that you want to look like a window on a spaceship. So you want to look at this “window” and see through it some “stars” (i.e. pinpoints of light) that appear to be at a near-infinite distance away. Of course, the stars are not really an infinite distance away, the effect needs to be created using a series of mirrors/lenses/prisms/projector/etc behind the “window”.

Some other points to consider:

* There are several metres of space behind the “window”, so plenty of room to install whatever mirrors/lenses/prisms/projector/etc are needed to create the illusion
* This needs to look correct from different viewing positions, not just where the viewer is stationary.
* This doesn’t need to be a hologram, as there is only a (near) infinite distance that is needed
* This doesn't need to be perfect; if, for example, the "stars" appeared to be 50m away, that would be fine.

Can you help or throw some ideas out there?

 

[berkeman]

* This needs to look correct from different viewing positions, not just where the viewer is stationary.

Can you give more quantitative specs for this please? What is the viewing area that you need this to work over? If you could give all the dimensions of the setup, including the Object area and the Image area and the Window dimensions, that would help a lot.

Obviously HUDs work well for this, but over a small Image area.

 

[Drakkith]

Let's start with a simple example. You want a single 'star' to appear as if it is an infinite distance away. This would be as simple as placing the light source at the focal point of a positive lens, which causes the emitted light to exit the lens parallel to itself, making its apparent distance infinite.

The problem you're faced with is how to scale something like this up to a large size and to a rather wide viewing angle. Telescopes also make things appear at an infinite distance away and can achieve greater than a 100 degree viewing angle with expensive eyepieces, but they are limited to small eyepieces that sort of 'wrap around' the viewers eye (see how the rightmost lens in the diagram below is concave, with the observers eye looking left). An example of this is the Nagler eyepiece design, shown here:

My first thought is to embed your light sources into a concave surface and then place a large lens system between them and the window. The concave surface would be at the lens system's focal plane (which is curved), helping to suppress aberrations. The problem with this design is that the lenses might have to be absolutely massive.

A more likely alternative would be to use mirrors. Mirrors are far more lightweight, though they suffer from the unfortunate property that they aren't transparent and will have to be offset to avoid blocking the light. At a minimum, you'll need a mirror somewhat larger than the window, as viewers looking through the window at an oblique angle will still need to 'see' the mirror (aka, have line of sight with the light sources, which bounce off the mirror). Exactly how big will depend entirely on the specifics of the setup.

You could probably get away with using a single paraboloidal (often called parabolic) mirror, but you'll have significant aberrations the farther off-axis the viewer looks. A more complex setup would give better results, but, as stated, would be more complex. The size of the light sources, number of optical elements, spacing between elements, mirror curvature and shape, and all other properties are completely open ended. There are likely a very wide range of values for all of these that would work and its up to you to determine exactly what you need based on your project specifics.

 

[simonlhill]

Thank you so much for your quick responses and please accept my apologies for the question being so open-ended. That was intentional, as I didn't want to overly complicate this just yet.

In fact, the intention in the end was to scale this up to a "window" that was 3 -4m wide and 2m high. The hope was the viewer would be able to walk around this (so between 1m and 10m away from the window but standing to the left or to the right of it) and to still get the effect of pins of light at or near to infinity. The intention is for there to be 10 or 20 pins of light in total; really, everything else could be determined to make this look as realistic as possible. @berkeman, I hope this helps.

@Drakkith, thank you so much. I was thinking similar, i.e. this would be relatively easy if the viewing hole was small, but given this is a large window, the lens would need to be immense and so this probably comes down to how mirrors could be used instead. For example, I was thinking the light sources could even be behind and above the "window" pointing downwards towards a mirror at 45 degrees (and with some kind of parabolic shape) across the whole window. Hope that makes sense!

You mentioned a more complex set-up. Might you be able to please advise what something like this might be?

 

[Drakkith]

You mentioned a more complex set-up. Might you be able to please advise what something like this might be?

A single mirror will introduce multiple aberrations that cannot be corrected for, as the available free variables by which to correct these aberrations is very low. A single paraboloidal mirror has many aberrations, of which the most prominent is coma, an off-axis aberration that causes objects viewed off the optical axis (so looking at the mirror at an angle and not straight on) to blur. By splitting the power and focusing between multiple optical elements each element can be tailored to correct for one or more aberrations. The end result is that the more elements you use, the better looking the final image can be, with the obvious caveat that more elements is more expense, weight, size, and complexity.

Note that I'm not a professional optical engineer (though I went to school for a few years to be one before dropping out due to health issues). There might be a much more compact/simpler/better way of doing what you want that I simply don't know about.

If you're serious about your design, I encourage you to start much smaller so you'll be able to get a feel for what works and what doesn't without all the expense of a larger project. Optical systems can almost always be scaled up without too much trouble if I remember one of my textbooks correctly.

 

[tech99]

I think a good illusion to use for this is Pepper's Ghost, used on stage, and described in this Wiki article. It uses a sheet of glass at an angle, which is itself invisible, but reflects the image when it is illuminated.
https://en.wikipedia.org/wiki/Pepper's_ghost

 

[simonlhill]

@Drakkith, thank you so much for that. Yes, that's why I was trying to do this with a small window first. Then I'd scale it up to the much larger window for the final project.

@tech99, thanks! I know Pepper's Ghost, but I don't think that would work as I'm wanting the image to appear at (near) infinity. Pepper's Ghost would result in the image appearing a finite (near) distance away. Or is there some way to make this appear at infinity?

@berkeman, did the extra information help? You mentioned HUD, so I imagine you were thinking of some kind of collimator and combiner, but that's tricky as the window needs to be so wide. Any thoughts on that?

 

[sophiecentaur]

I know Pepper's Ghost, but I don't think that would work as I'm wanting the image to appear at (near) infinity.

If you wanted the ghost to appear at infinity then you are saying that you want the parallax of the image to make it seem to be at infinity. If you used a sensor to tell your position in the room then a servo could adjust the angle (and position) of the pepper's mirror to keep the image in the right place for the infinity illusion to work on you. BUT it would only work for you and no one else in the room.

I reckon that could be a good basis for a project but it may not be within the terms that you want. Simple optics would only work for a vast setup, I think.

 

[simonlhill]

@sophiecentaur Thank you very much for this. Yes, I've seen that done before, but as you say, the issue is it only works for one person in the room.