Use a Hologram of a lens as a lens?

[cadcoke5]

I am somewhat of a novice, but have read a lot about holograms over the years.

I know there is something called a "Holographic Optical Element". These are currently available as rear-screen projection systems, which accept light from a video projector, and then diffuse it towards the audience, while still being transparent. I suspect these may simply be a transmission hologram of a large white sheet. In use, the video projector simply occupies the position of the reference beam.

Many years ago I read that a hologram of a lens will act like a lens. However, I am not clear if this means that just the objects present when the hologram was created could be seen through the lens,or perhaps real-world objects later looked at through the hologram would also be modified by the lens. There may also be restrictions such as only using light the color of the original laser.

Can I simply make a transmission hologram of a lens and then use it like a lens?

Joe Dunfee

[holorefugee]

The short answer is yes. The long answer is the angle of the reference beam and object beam cause limitations.

[Martin]

The short answer is yes. The long answer is the angle of the reference beam and object beam cause limitations.

...and not to forget chromatic dispersion. The (transmission) HOE will only work "like a lens" in a monochromatic environment.

[Johnfp]

Dave B has an awsome photo of a hologram he made of a lens and he is standing behind the hologram (I think) and you can see most of his face normal and some of it though the HOE and it is reduced in size.

[holorefugee]

The short answer is yes. The long answer is the angle of the reference beam and object beam cause limitations.

...and not to forget chromatic dispersion. The (transmission) HOE will only work "like a lens" in a monochromatic environment.

Yes, to make the HOE select wavelength it must be made in reflection. Otherwise it is only useful for laser light.

[Dinesh]

Can I simply make a transmission hologram of a lens and then use it like a lens?

Joe Dunfee

No, depending on what you mean by "transmission hologram of a lens". If you shone light onto a lens at some random angle, such that the glass of the lens reflected some light back onto the plate, thus collecting scattered light from the front surface(s) of a lens, then it would be a hologram of a lens. When you reconstructed the hologram, you'd see a lens as the image. This would not focus light since the focusing effect depends on the curvature of the surfaces of the lens, which you have not captured. All you've captured is the light reflected from the glass surfaces of the lens You could even make what's called a "shadowgram" of the lens, which could be a better "hologram of a lens".

To make a lens hologram, ie to make the hologram act as a lens, you need to capture the "shape" of the light that the lens produces when it's used as a lens. You'd need to pass light through the lens and used this light as the object beam. The "object beam" of the hologram is a pure, convergent (or divergent) beam of light and this will reconstruct as a pure convergent (or divergent) beam of light. When you look into the hologram you won't see an image of anything. The "image" is just pure light. Of course, as Martin mentions, there will be dispersion etc.

To make it narrow band, ie to make a transmissive lens and use it with white light, the holographic medium must be very thick. Even reflective HOEs have dispersion, especially when made with dcg(a problem I happen to be struggling with right now, as it happens!)

[BobH]

[
No, depending on what you mean by "transmission hologram of a lens". If you shone light onto a lens at some random angle, such that the glass of the lens reflected some light back onto the plate, thus collecting scattered light from the front surface(s) of a lens, then it would be a hologram of a lens. When you reconstructed the hologram, you'd see a lens as the image. This would not focus light since the focusing effect depends on the curvature of the surfaces of the lens, which you have not captured. All you've captured is the light reflected from the glass surfaces of the lens You could even make what's called a "shadowgram" of the lens, which could be a better "hologram of a lens".

If one made a transmission hologram of the reflection off a curved surface (like that off an uncoated glass lens), the hologram would indeed act like a lens. Maybe not with the same properties of the original glass lens, because only the power of the one curved surface is recorded, but still a lens. Same as making a hologram of a curved mirror.

[Dinesh]

Same as making a hologram of a curved mirror.

I think that's the crucial difference. I don't think that recording the phase wavefronts from the reflection in the geometry you mention is the same as "making a hologram of a mirror". In one case, the making of the hologram, you're imaging the mirror, in the other case, recording the phase wavefronts, your recording a phase profile.

If, by "making a hologram" of a mirror or a lens, you mean imaging the lens or mirror, for example by using shadowgram techniques or scattering light off the mirror or lens, then the hologram cannot focus light by diffractive methods as the original optic would do by refraction techniques (by "focusing", I mean both negative and positive focusing).If you looked into such a hologram, you'd see an image of a lens or mirror. However, if the mirror or lens were used as a focusing optic and the phase wavefronts of the lens (or mirror) were recorded, then the reconstruction beam would re-create an abstract phase wavefront. Looking into the hologram, you would not see an image of a lens (or mirror).

Thus, two plane wavefronts impinging on a hologarphic medium from opposite sides at different angles (say, 20 degrees to the plate normal on one side and 40 degrees to the plate normal on the other side) would be a holographic mirror. No actual mirror need be involved (you could use the collimated output of lenses to create the plane wavefronts). In this case, a plane wavefront with a particular frequency impinging onto the plate at 20 degrees to the normal would give, as an output, a plane beam at 40 degrees to the normal. The hologram itself would appear as a piece of clear glass (ideally!) with no visible image in it. But if I scatter light off a real mirror (by lightly crazing it's surface, for example) and used the scattered light from the mirror as my object light, then there'd be an image of a mirror in the hologram.

[BobH]

I understand the point you're making Dinesh, but the OP's original question didn't specify that the recording of the lens must perform exactly like the original lens. For example however, consider making a "focused image" hologram of a simple lens transilluminated by laser light coming from its focal point and completely filling the lens. Use a plane wave for the reference beam and an appropriate lens to image the subject matter lens into the recording plane. What you'd have is an off-axis version of the original, subject matter lens. One could then make a matching grating to use in front of this hologram and end up with a replica of the original lens, made using the original lens as the "object". Pretty convoluted, but possible.

[Dinesh]

Pretty convoluted, but possible

What do you think I'm busy doing right now
Just joking!

I was trying to answer the essence of the question (as I thought of it) that the OP seemed to confuse the image of an optic with the properties of an optic. "Simply" making an image of an optic will not reproduce the properties of an optic. I've noticed over the years that a lot of people are confused about this.

However, it's possible to make an image of an optic that does reproduce the properties also. In fact, if you did what you suggest, but made the grating a reflective grating, you'd have a (very odd!) image of a lens acting like a mirror. In fact, at POC I made a converging lens to reconstruct on the convex side of a glass surface. Thus, the glass bulged outwards, but focused inwards. Goodman (of "Fourier Optics" fame) visited us and saw this. He looked really puzzled and asked how the light focused "backwards"