Question about zooming out with optical lens

I need some help. I am working on a project and I am wondering if it is possible to make an object to look 100 times far away than it is actually using lens (or more than one lens). The lens (or lenses) should be near the object, not near the eye. For example if we have lens in front of an object that is 20cm away from the eye to make it visible as it is 2000cm away. I did some research and understood that i might need concave lens but I am not sure how to calculate the specification of the lens that will zoom out as much as i need and if it is possible at all to zoom out that much. I will appreciate any help! Thanks!

Edit: Sorry for the confusing question, here is more clarification. What I need is to use it in AR (augmented reality) project where the user will be looking at distance with transparent glasses and there will be either a projection or reflection from 20cm away to the glasses but user needs to be able to focus the wall which is 2000cm away and at the same time focus that projection/reflection from 20cm away. Thanks again for all your help! i really appreciate it. I believe it should be possible because HoloLens (Microsoft) is doing it.

• What you want exactly: 1. The eye focuses far away to look at it; 2. The object appear small; 3. The object appears with a "far away" perspective; 4. all three? Commented Sep 5, 2019 at 6:45
• @patta, number three basically is impossible. A different lens can't make the camera see the scene as it would appear when viewed from a different place, and your "perspective" is determined entirely by the place from which you view the scene. Commented Sep 5, 2019 at 12:43
• @patta sorry for my confusing and not well formed question. I think I need number #1 - The eye to focus far away to look at it. What I need is to use it in AR (argument reality) project where the user will be looking at distance with transparent glasses and there will be either a projection or reflection from 20cm away to the glasses but user needs to be able to focus the wall which is 2000cm away and at the same time focus that projection/reflection from 20cm away. Thanks again for all your help! i really appreciate it. I believe it should be possible because HoloLens (Microsoft) is doing it Commented Sep 5, 2019 at 13:13
• @Solomon Slow, yes I think it is possible, with a telecentric lens (perspective as from infinity) plus an eyepiece. 1000's of \$ and some kg of lenses.. Commented Sep 5, 2019 at 17:57
• @patta, For benefit of other readers who may not know, an object space telecentric lens basically only admits rays that are parallel to the lens axis. If you want a picture of a whole object, then the object must be smaller than the front element of the lens. The image of the object will be the same size on the sensor no matter how far the object is from the lens. I guess that's a possibility that I wasn't thinking of when I made my earlier comment. Commented Sep 5, 2019 at 19:51

Hei so, the short answer is: you need a Positive lens with focal length about equal to the distance lens-screen; like the Virtual Reality goggles.

I will try to add some detail and links, today is impossible because my sole source of wisdom, Wikipedia, is DOWN.

Formula, I will say something like: the focal lenght should be $$f= b / (1 - \frac{a}{d})$$ ; since a is much smaller than d, f is about equal to b. Also, you cannot have the lens really near the screen; or you need a very powerful lens, not recommended. Half-way is ok.

I made a drawing to explain how the Microsoft Holo Lens work:

1. Start with the VR goggles; a positive lens focus on the nearby (phone) screen, while the eye thinks is looking far away.
2. Add a BeamSplitter at 45 deg to merge real image and VR; half of the light goes trough straight to the real object, the other half is reflected up to the VR lens and screen. Here the Beamsplitter is a simple glass panel. The eye see the real object and "at the same distance", superimposed, the screen image.
3. Instead of a glass panel, two prisms work better; the first reflects half of the light, the second fix the direction of the rays going to the real object
4. Somebody had the idea of making the reflecting surface Concave, so is like a positive converging mirror; it acts as a lens itself, the extra lens is no more needed. It is like an Off-axis Newtonian telescope.
5. To reduce optical problems of the previous solution (and get wider field) they put a second (slightly divergent) mirror; the system is still positive. It is like an (off-axis) Cassegrain telescope.
6. With apparent ease, they used the same first surface as the second mirror.

So if you are making it yourself I recommend the level 2. As lenses, you can use: VR goggles / Reading glasses +6.00 /2x Fresnel plastic lenses. As beamsplitter, a flat pane of glass will do. A pair of microscope glasses f.eks. Only issue will be "double reflection"; if you don't like it you have to get the prisms. I found only one link of DIY hololens; he used a second mirror on top:Link with few specs

I tried a fast setup for your pleasure; with credit card size Fresnel lens. See the double reflection from the 2,5mm thick glass pane; the focus hologram-reality is not quithe there, let's blame the phone camera.

Edit1: at point 2. it seems that light originate from the eye; that is not the case: light comes from the object and the screen; 50% of the light coming from the object goes through the beamsplitter and reach the eye; the other 50% is reflected down and wasted. The light from the screen, 50% is reflected by the beamsplitter and reach the eye; the remaining 50% goes straight down and get wasted.

Edit 2: focusing: The screen and lens position are adjusted such the eye can focus at the same time the real object and the image on the screen (they appear at the same distance). The HoloLens can recognize what external object you are looking at, measure its actual distance, adjust the position of the screen so when your eye is focused at the object, also the hologram image from the screen is in focus. a) hologram position and focus mismatch; b) hologram position fixed by moving the image on the scren; c) hologram focus fixed by moving the screen in focus. Sorry again for the light rays starting from the eye...

Edit 3

Another system for mixed reality, pre-digital, is the Intermediate Focus. In a telescope you have a virtual image plane, and it is possible to insert there a transparent screen; seen from the eyepiece, the image of the screen will appear in focus and superimposed to the image from outside.

Examples of this are: the crosshair of gun scopes; the viewfinder info bar in reflex cameras; the fluorescent screen in night-vision devices.

Intermediate focus system needs more lenses than the beamsplitter system (objective lens, erector prisms/lenses, eyepiece lenses) and the choice of see-through digital screens is probably limited. And the eye-monitoring system of the HoloLens must be modified.

Advantages can be: possibility to have dark holograms (impossible with HoloLens); can easily attain wide angle view and full-view hologram; can manipulate light coming from outside (as night vision); 100% (theoretical) external light transmission.

• your answer is outstanding with so detailed explanation, illustrations and even photos. I am so thankful for your time and efforts! Thank you so much! I have to still read it few more times to understand it fully and then may be try to build it. I am a software engineer and I live and work in Los Angeles, California and I am trying to build a very interesting startup. Is there a way to contact you in private via skype or messenger (or any other way that you prefer)? I would like to talk to you in private about it but couldn't find a way in stackexchange website to send you a message. Commented Sep 7, 2019 at 1:50
• also seems like the screen reflection view will float much closer than the real object (a+b<d). Do you think user can focus at the real object (far away, d) and have the screen focused at the same time (i.e. screen can be visible as it is in d distance)? Because that is the main goal to do so user can focus both in far away distance equal to d. Commented Sep 7, 2019 at 3:02
• chat.stackexchange.com/rooms/98392/holo-lens-design Commented Sep 7, 2019 at 8:30
• Yes, the image and object can look like at the same distance; this job is done by the lens in 2-3. The rough formula at the beginning should make both screen and object in focus. To do in reality it is hard, because the eye change focus when looking at near or far objects, so also the hologram must be optically adapted (focused) to look near or far; and you need to monitor where the eye is looking. Commented Sep 7, 2019 at 10:20
• Hei, tell me, see the chat link above Commented Sep 8, 2019 at 11:01

The lens type you need is called an ultra wide angle lens. the "widest" lens of this sort is a "fisheye" lens with an acceptance angle of 180 degrees, but these create significant amounts of image distortion. There are "near-fisheye" lenses with smaller acceptance angles and almost no fisheye distortion; one of these will make the subject in the image appear to be very far away.

• FYI: Fisheye lenses have been made with a wider field of view than 180 degrees. petapixel.com/2012/04/24/… Commented Sep 5, 2019 at 13:09
• Sorry for my confusing question, please see my edit above for more details what exactly i need. Commented Sep 5, 2019 at 13:36
• @niels nielsen, thanks for your answer, i believe the image distortion can be fixed on software level the way the vr headsets are doing. But how do you set the object focus distance to be further away with ultra wide lens so user can focus at the same time on object 2000cm away and on the close object through lens that is 20cm away? Is it depending on the angle or is there a maximum that cannot be passed? Thanks! Commented Sep 6, 2019 at 13:26