- #1

BiGyElLoWhAt

Gold Member

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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.