You are recording an in – line hologram with an object inscribed on a transparent sheet. Mathematically represent the recording and reconstruction of the holograms, and draw a neatly labelled diagram. What will happen if the reconstruction wavelength is two times larger than the recording wavelength. How to record a holographic converging lens? ( 6 marks )

Answer

In-line Holography Recording and Holographic Lens | StudyHW

In-line Holography: Recording and Reconstruction Explained

📌 Recording an In-line Hologram

In in-line holography, the object is illuminated by a coherent monochromatic light (such as from a laser). The light that passes directly through the transparent sheet acts as the reference wave \( R(x, y) \), and the light diffracted by the object acts as the object wave \( O(x, y) \).

H(x, y) = |R(x, y) + O(x, y)|^2

This equation represents the hologram intensity pattern recorded on the photosensitive medium. The recorded interference pattern contains both amplitude and phase information about the object.

Figure: Setup for recording an in-line hologram

🔁 Reconstruction of the Hologram

To reconstruct the image, the hologram is illuminated with a reference wave identical to the one used during recording. The diffraction of this light recreates the original wavefronts.

Reconstructed\ wave = H(x, y) × R(x, y)

This results in:

A real image of the object at the original object location.
A virtual image behind the hologram plane.

🌈 Effect of Using a Reconstruction Wavelength Twice the Recording Wavelength

If the reconstruction wavelength \( \lambda_r \) is twice the recording wavelength \( \lambda_0 \), then:

The reconstructed image will be blurred and its position will shift. Specifically:

The virtual image appears farther from the hologram.
The image size will be magnified approximately by a factor of 2.
The sharpness and fidelity of the image will decrease.

🔬 Recording a Holographic Converging Lens

To create a holographic lens, follow this method:

Place a point source (acting as the object) at a specific distance from the photosensitive plate.
Illuminate the plate with a plane reference wave from a laser.
The resulting interference pattern will encode a lens-like structure in the hologram.
Upon reconstruction with the same reference wave, the hologram behaves like a converging lens.

This is commonly used in holographic optical elements (HOEs) for beam shaping, collimation, and focusing in optical systems.

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