Holography records the interference pattern between a reference beam and light coming from an object. Unlike ordinary photography, holography stores both intensity and phase information indirectly through the fringe structure recorded on the plate or photosensitive material.
In a simple two-beam geometry, the reference beam and object beam cross at an angle \(\theta\). The resulting interference fringes have spacing
\[
d_f=\frac{\lambda}{2\sin(\theta/2)}.
\]
If the recording takes place inside a medium of refractive index \(n\), the effective wavelength becomes
\[
\lambda_{\text{med}}=\frac{\lambda}{n},
\]
so a more general version is
\[
d_f=\frac{\lambda_{\text{med}}}{2\sin(\theta/2)}.
\]
This formula shows that fringe spacing becomes smaller when the beam angle becomes larger. A wide-angle geometry creates tightly packed fringes, while a small-angle geometry creates broader fringes. Since the recorded pattern is extremely fine, holography typically requires coherent laser light.
For the sample values
\[
\theta=30^\circ,\qquad \lambda=633\text{ nm},\qquad n=1,
\]
the fringe spacing is
\[
d_f=\frac{633\text{ nm}}{2\sin(15^\circ)}.
\]
Using \(\sin 15^\circ \approx 0.2588\),
\[
d_f \approx \frac{633}{0.5176}\text{ nm}\approx 1223\text{ nm}.
\]
Therefore,
\[
d_f \approx 1.22\,\mu\text{m}.
\]
This is the expected result for the HeNe laser example.
The corresponding spatial frequency of the recorded pattern is
\[
\nu=\frac{1}{d_f}.
\]
A smaller fringe spacing means a larger spatial frequency, which implies a denser recorded pattern on the holographic plate.
During reconstruction, the hologram is illuminated again, usually with a beam similar to the original reference beam. The recorded interference pattern diffracts the reconstruction beam and regenerates a wavefront related to the original object beam. This is what gives holography its three-dimensional appearance.
If the reconstruction angle differs too much from the recording reference angle, the reconstructed image can shift, distort, or appear less accurate. That is why simple holography demonstrations often emphasize matching the reconstruction geometry to the recording geometry.
At more advanced level, one studies volume holograms, Bragg selectivity, and thick-medium effects. But the basic two-beam interference model used here is the correct starting point for understanding how holographic fringe patterns are recorded and why coherent beams at a chosen angle create a finely spaced interference structure.
This calculator uses that simple model. It computes fringe spacing, spatial frequency, and a basic reconstruction mismatch measure, while the graph and animation help visualize the recorded interference pattern and the reconstruction concept.
