B Intuitive, conceptual understanding of holography

[BiGyElLoWhAt]

I'm trying to understand how optical holography works. I made a hologram using LitiHolo C_RT20 instant develop hologram film and am now trying to understand how this actually works. It almost makes sense to me. What I'm having trouble understanding, however, is this:
Reference wave + object wave = speckle on the film. Speckle + reference wave = object wave?
This feels very counter intuitive to me. I looked through the wikipedia page here, and everything follows, but the end result is very lack-luster. It's not intuitively obvious to me that what you get at the end resembles the object wave.

From the article:
$\mathbf{t} A_\text{R} \exp {i \varphi_\text{R}} = \left[ \mathbf{t}_0 + \beta \left[ A_\text{R}^2 + A_\text{O}^2 + A_\text{R}A_\text{O} \exp {i (\varphi_\text{R} - \varphi_\text{O})} + A_\text{R}A_\text{O} \exp{-i (\varphi_\text{R} - \varphi_\text{O})}\right]\right] A_\text{R} \exp {i \varphi_\text{R}}$
This can be split into three terms:
$\begin{align} \mathbf{U}_1 &= \left[\mathbf{t}_0 + \beta A_\text{R}^2 + \beta A_\text{O}^2\right] A_\text{R} \exp {i \varphi_\text{R}} \\ \mathbf{U}_2 &= \beta A_\text{R}^2 A_\text{O} \exp i\varphi _\text{O} \\ \mathbf{U}_3 &= \beta A_\text{R}^2 A_\text{O} \exp{i (2 \varphi_\text{R}- \varphi_\text{O})} \end{align}$

$\mathbf{U}_1$ is a modified version of the reference wave. The first term is a reduced amplitude version, the second is also a reduced amplitude version if the reference wave amplitude is uniform. The third term produces a halo round the transmitted reference wave which is negligible when the amplitude of the object wave is much less than that of the reference wave

$\mathbf{U}_2$ is the reconstructed object wave which is identical to the original wave except that its amplitude is reduced. When the object wave is generated by light scattered from an object or objects, a virtual image of the object(s) is formed when a lens is placed in the reconstructed wave.

$\mathbf{U}_3$ is known as the conjugate wave. It is similar to the object wave but has the opposite curvature. When the object wave is generated by light scattered from an object or a series of objects, a real image is formed on the opposite side of the hologram plate to where the object was located and is deflected from the normal axis by twice the angle between the reference wave and the normal direction.

 

[.Scott]

Decades ago, in college, I had fun in the laser lab doing holograms.
At the intuitive level, I always looked at it as wave front reconstruction.
Of course, the film is a negative, so technically, you are reconstructing a wavefront that is 180 degrees out of phase - but that doesn't change the amplitudes or the way the wavefront progresses.

What the film is capturing is the objective wave and reference wave phase differences. Where they are the same, there is constructive interference and the film is darkened. Where they are the directly out of phase, there is destructive interference and the film ends up transparent. So when the reference wave illuminates the developed film, the selective transparency results in a reconstructed wavefront - all be it 180 degrees out of phase from the original.

I hope you are enjoying the experiments. I stayed up into the wee hours creating holograms that really showed the 3-D effects. In one case, after spending a few frustrating hours trying to project a real image of a vacuum tube, I slouched back in my chair to see the mirror image of the printing on the tube directly in front of my face. For an instant, I wondered how I managed to get myself inside the tube. So I packed up and went back to my dorm room for some needed sleep.

 

[Andy Resnick]

I'm trying to understand how optical holography works. I made a hologram using LitiHolo C_RT20 instant develop hologram film and am now trying to understand how this actually works. It almost makes sense to me. What I'm having trouble understanding, however, is this:
Reference wave + object wave = speckle on the film. Speckle + reference wave = object wave?
This feels very counter intuitive to me. I looked through the wikipedia page here, and everything follows, but the end result is very lack-luster. It's not intuitively obvious to me that what you get at the end resembles the object wave.

I've used the LitiHolo system as well, it's great!

Holography is also called 'wavefront reconstruction', because that's what happens when you illuminate the hologram properly. The pattern on the film is indeed an interference pattern (what you call 'speckle' is a spatial interference pattern), and so phase information is retained in the hologram pattern. By illuminating the interference pattern with the reference beam, the 'original' object wavefront is reconstructed, generating a wavefront that appears to have been generated by the object (when in fact is it is generated by the interference between the hologram pattern and a new reference beam).

There are some subtleties here, so I encourage you to play around!

 

[BiGyElLoWhAt]

Ahhh. @.Scott
I think the piece I was missing was the negative. So basically I was looking at wave 1 + wave 2 = interference. Interference + wave 1 = wave 2, but that doesn't make sense. It should be Interference - wave 1 = wave 2. However I'm more so looking at wave 1 + wave 2 = -interference -> -wave 1 -wave 2 = interference. interference + wave 1 = - wave 2, but we don't care about the negative sign because our eyes don't distinguish phase.
Pseudo qualitative math of course.
Thanks a lot.