Holographyforum.org / holowiki.org

There is a way of fooling the eye. If you have a horizontal disc containing a hologram, and illuminate it from below so that the image appears above the disc, it fools the eye to think that the object sits in free space. Of course, as Petr says, your vision is limited to the area of the disc, but most people seeing the illusion aren't aware of this. It isn't real time, you have to pre-record the hologram. But, so many people started to call it the "Leia" illusion, that we just ended up calling this our :Leia display.

https://www.youtube.com/watch?v=zgcKKgQPjuw
https://www.youtube.com/watch?v=1Nq4ri2t-HI

If you mean the display with the terrain from the film Avatar (https://james-camerons-avatar.fandom.com/wiki/Operations_Center), this is hardly possible with classical holography. If fact, illusions floating in the air above an table are still possible just in sci-fi. I am not aware of any pysical principle that could potentially make it.
Simple explanation: when you see a ball, light ray from a ball must hit your eye. When you want an illusion of a ball, the light ray still must originate somewhere. As a light ray cannot turn on its own, it follows that the light source ("a display") must be in line with your eye and the ball illusion. Thus, it is possible to make an illusion floating in front of some display, say a conventional hologram. But if you want to watch such an illusion "from side", it disappears as a light ray starting on the dispay surface have no way to reach both the illusion AND your eye.
Moreover: if you find a way how to bend a ray at a given point in the air (such as projection into fog), you have no way to block other light from passing that point. This means that the illusion is transparent, it cannot cover neither other parts of the illusion nor any real object.

I dont need to see interference lines. I wanna know of possibility making holographic display as shown on "avatar". I think we could make holographic "object" in space if behaviors of the film and empty space in a place were film is supposed to be are simillar. Is is it so or not?

It depends on what you mean by "real time". If you set up a real object, illuminate it with a laser, and let the laser light hit a white card, then you put a reference beam on the white card, you will not see interference lines on the white card because they're too small. Usually, the number of interference lines are denoted by the spatial frequency, and, typically, spatial frequencies are in the order of 1000 lines/mm.

You can see a "real time" hologram if you make a hologram in the traditional way, replace the hologram, with the object still in place, reconstruct the hologram and slightly disturb the object. Now, the wavefront from the original hologram and the wavefront from the reconstructed hologram are slightly out of phase, and you get a beat frequency.

I agree that fringe system is 3D, but I meant the intersection of two fronts. I see it as hyperbola.
I didn’t understand why it is impossible to demonstrate a hologram in real time? Due to air fluctuations or it is principally impossible? You didnt explain.

The fringe system is actually 3 dimensional, they're hyperboloids, not hyperbolae. If the system is just 2-dimensional - across one plane - then only one line across the film would expose.

[quote=Ytre post_id=72124 time=1603017737 user_id=7753]
Is it possible to demonstrate a hologram in real time without using film?
[/quote]
It's not possible to demonstrate an actual object, because the spatial frequency is high, ie the spacing between fringe lines is small, in the order of microns. If you look at the above equation, λ = d*sin(θ), you'll see that even with a 10 degree beam separation, the lines are spaced at 7 microns, too close to see with the unaided eye (in comparison, a human hair is about 25 microns wide). It's always possible to observe interference lines with any interferometer. In fact, most holographers test the stability of their system using a Michelson interferometer. In a Michelson interferometer, the two beams are inline, ie the interbeam angle is close to zero. So you can see the lines on a wall. If you want to see the effect of changing the angle between the two beams, you can tilt one of the mirrors in the interferometer.

It is not entirely clear from this figure, but I understood principal of how hyperboles are formed. If both waves were spherical, then the hyperbola would lie in the plane perpendicular to the film, and in the case of one plane wave it is in the plane of film. I got it. Is it possible to demonstrate a hologram in real time without using film? After all, the effect will be exactly the same as with the film, i.e. in the plane of space, the same patterns will form and the maximums will be the place of formation of spherical waves. Or not?

If you have two point sources, as in your diagram, then you will get a sinusoidal variation of light bands and dark bands. The defining equations is:

m*λ = d*sin(θ)

where m is called the 'order' of the pattern (the pattern repeats - dark, light, dark, light etc) ), d is the distance between two slits, λ is the wavelength and θ is the angle between any point on the screen and a normal (straight line) from half way between the slits. So, let us say that you set up your two slits (if you're using a laser, you don't need the first slit) separated by 0.02 mm and you measure the third bright point on your screen to be at an angle of 5.45 degrees from the centre of the slit system, what is the wavelength?

λ = d*sin(θ)/m = {(0.02)*sin(5.45)}/3 = 0.000633

The intensity variation is sinusoidal, and is given by

I(t) = 4*I* cos²(θ/2)
where I(t) is the total intensity at the screen, and I is the intensity at each slit. So, if you imagine a cos² curve, the fringe system follows the curve.

This is for a two slit system, as you've drawn. However, in holography, we usually have a planar (flat) wave and a diverging wave from a point source. In this case, the fringe system is hyperbolic, the lines of equal intensity are shaped like hyperbolas. Depending on where you place the film, the film will intersect the hyperbolas and form the fringe system. Below is a diagram from "Optical Holography" by Collier, Lin and Burckhardt

[attachment=0]fringes.jpg[/attachment]

[quote=Ytre post_id=72115 time=1602878591 user_id=7753]
I dont understand what did you mean by hyperbola? Is it projection on film? Could you explain it in detail?
[/quote]

https://en.wikipedia.org/wiki/Hyperbola

It seems I have imagined it correctly. Its because of spherical fronts in space they intersect each other. Ok. I have it now understood at last.