Text Projection in Smart Glasses

Question

Say I have a pair of glasses such that each lens is densely pixelated and each pixel can be controlled to block (or attenuate) light coming through.

Can I use this technology to project text (say "Hello World") to appear 10 meters away? Or do I also have to control the phase of the light coming through somehow?

Edit: First, a clarification, the lenses I were referring to are the eyeglasses lenses which serve no optical purpose (focus, etc.) other than having them able to attenuate light at certain "pixels".

Now, Lets imagine I really hold a sign 10 meters away from me with the text "Hello Word", somehow the light propagates through the eyeglasses and reach my eyes forming the image I want to "artificially" create. Now if I measure the wave (amplitude and phase, say per wavelength) at each pixel going through the eyeglasses then of course I can recreate the "Hello World" sign if I can manipulate the amplitude and phase per pixel, but I guess, after reading the comments, doing this by just manipulating the amplitude wont work because I won't be able to create the focus of the text on the retina since the phase control is equivalent to having optical elements such as mirrors, lenses etc...

Answer 1

Making something look like it's floating 10m in front of the viewer can be based on our stereo view. Both eyes need a little different image in front of them. But those images must be sharp. They can be quite near of observer's eyes if he has magnifying lenses between the images and the eyes - like the common virtual reality hoods. The image is not in the lenses, it's on flat displays which are watched through the magnifying glasses which should be made of clear material.

If you want to see the real scene (as real, not projected to the display) at the same time as the generated image, the generated image must be so far away in front of you that your eye sees it sharp without a magnifying glass and the unused area of the display must be transparent. That's about 0,5 meters or more. Quite a big high technology display is needed for realistic size items. You still need some shutter system to keep off the left eye image from the right eye and vice versa. It's solved to some degree in 3D movies.

Unfortunately I do not know enough of holograms. I can only guess that holography could give a way to generate sharp looking realistic images with a device placed at short distance in front of the eyes and it still shows also the real scene as sharp because no magnifying glass is needed - the light comes to the eye from a working hologram just like the object was 10 meters away.

Holograms mean also controlling the phases of the lightwaves. They are high density phased arrays of radiators. You need R, G and B wavelength versions of them for both eyes. Controllable phases can be created with lasers.

I'm afraid we do not have a practical way to control the needed amount of nanometer scale pixels; the pixels really must be a fraction of the wavelength of light because otherwise they cannot create the needed diffraction.

Although not practical today, holographic displays are under development. Search for "Holographic display" to see what's claimed to have been invented.

ADD You lately inserted a clarification note which says

the lenses I were referring to are the eyeglasses lenses which serve no optical purpose (focus, etc.) other than having them able to attenuate light at certain "pixels".

Those lenses really can display an image like LCD displays do. If the background light source is the environment the display could also allow you watch the environment at the same time. Your eyes cannot see as sharp at the same time both the image on the glasses (=distance about 0,5...1 inch) and what's coming through them. Many of us wouldn't at all see the image on the glasses as sharp without having a magnifying glass between the eye and the image.

I guess you are interested does the exist a way to blur the image on the glasses in such way that the unsharpness caused by too close watching distance just reverses that blur. I'm afraid that a proper mathematician and a good model of the imaging in the eye are needed to give the solution. Elementary math says that a lens - also the lens of your eye - makes a linear transformation and many linear transformations have an exact reverse transformation. But it's totally beyond my knowledge

• what is such proper model of the eye,
• how one should take into the account nonlinearities in the sight process and the fact that a filter in front of the eye actually doesn't add, it multiplies and
• how to generate in a controlled way both positive and negative light in the reversely blurred image (if such thing exists).

This lecture http://6.869.csail.mit.edu/fa16/lecture/lecture3linearfilters.pdf

presents blurring and reversing blurs in the most elementary form. If you can read it you maybe are able to find and understand also some advanced works of the subject. They are beyond my capabilities.

I guess that reverse-blurring an already sharp image so that watching it from too short distance blurs it perfectly sharp needs infinite positive and negative light levels which makes it non-existent. But a mathematician is needed to prove it or to tell it's rubbish.

Answer 2

It's not the phase of the light that needs to be controlled. The image would need to be "drawn" on the retinas of each eye in a way to create visual disparity equal to that of a target at 10 meters.

Answer 3

If you mean literally, opaque and transparent LCD film on/inside a typical eyeglass lens, then no, this won't work.

Realize that our eyes can't focus on the lens itself - we focus several feet beyond. So anything the LCD "image" was displaying, would only appear as a very distorted, almost unrecognizable blur.

If you made the eyeglass lens stronger, you could put the LCD's maybe an inch or two further than the eyeglasses. Then you'd be able to focus on it - but now everything else will be out-of-focus.

Answer 4

The question is more confused after your edit.

First, a clarification, the lenses I were referring to are the eyeglasses lenses which serve no optical purpose (focus, etc.) other than having them able to attenuate light at certain "pixels".

So it would work like a projector LCD. OK.

Now, Lets imagine I really hold a sign 10 meters away from me with the text "Hello Word", somehow the light propagates through the eyeglasses and reach my eyes forming the image I want to "artificially" create.

But this would really be created. It's how our eyes work normally.

Now if I measure the wave (amplitude and phase, say per wavelength) at each pixel going through the eyeglasses ...

You can't. Light will be going through the glass from every angle. You're only thinking of the rays from the object to your retina. If you want to see what your eye sees then you would need a half-mirror and the camera looking through something like an SLR prism so that it sees what your eye sees. It's not clear how you would measure the "phase" of the light or what the phase is measured relative to. I suspect you may have used the wrong term.

... then of course I can recreate the "Hello World" sign if I can manipulate the amplitude and phase per pixel, ...

By "amplitude and phase per pixel" I presume you mean the LCD's pixel control.

... but I guess, after reading the comments, doing this by just manipulating the amplitude wont work because I won't be able to create the focus of the text on the retina ...

Correct.

... since the phase control is equivalent to having optical elements such as mirrors, lenses etc...

It's not clear what you mean here.

There are a bunch of problems. Your backlight source is the background of where you are looking. If this is dark then your image will be dark no matter what your LCD is doing.