In holography, a recording is made by interfering two coherent optical waves at a photosensitive plate or film.
One beam is usually called the reference beam, and the other is the object beam.
Their interference creates a fine pattern of bright and dark fringes that stores both amplitude and phase information about the object wave.
Unlike ordinary photography, which records only intensity, holography preserves the wavefront structure needed for three-dimensional reconstruction.
For two plane waves crossing at an angle \(\theta\), the interference fringes form a periodic grating.
The spacing \(d\) between neighboring fringes is
\[
d=\frac{\lambda}{2\sin(\theta/2)},
\]
where \(\lambda\) is the wavelength of the recording light.
This formula shows that the fringe spacing becomes smaller when the recording angle becomes larger.
If the two beams are almost parallel, then \(\theta\) is small and the fringes are widely spaced.
If the beams cross more sharply, the fringes become much denser.
The reciprocal of the fringe spacing is the spatial frequency of the recorded grating:
\[
\nu=\frac{1}{d}.
\]
This tells you how many fringes occur per unit length on the hologram.
A related quantity is the grating-vector magnitude
\[
K=\frac{2\pi}{d},
\]
which is useful in wave-vector descriptions of diffraction and holographic reconstruction.
The sample case in this calculator uses a HeNe wavelength of
\(\lambda=633\,\text{nm}\)
and a beam angle of
\(\theta=30^\circ\).
First compute the half-angle:
\[
\frac{\theta}{2}=15^\circ.
\]
Then the fringe spacing is
\[
d=\frac{633\times10^{-9}}{2\sin 15^\circ}
\approx 1.22\times10^{-6}\,\text{m}
=1.22\,\mu\text{m}.
\]
This is why holographic recordings can contain extremely fine spatial structure.
Even with visible light and only moderate beam angles, the grating spacing is on the micron scale.
During reconstruction, the recorded hologram is illuminated again.
If it is illuminated by a beam similar to the original reference beam, the hologram diffracts light to reproduce the original object wavefront.
To an observer, the wave appears to come from a virtual image, meaning the rays do not actually converge at the image location but appear to do so when extended backward.
This is one of the characteristic signatures of holography.
Another important possibility is phase-conjugate or conjugate reconstruction.
In that case, the reconstructed wave can form a real image, meaning the diffracted rays actually converge in space.
This is often described as a time-reversed or conjugate wavefront.
In a schematic treatment, same-reference reconstruction is associated with virtual-image viewing, while conjugate reconstruction is associated with a real-image path.
The simple two-beam fringe formula used here assumes a basic thin holographic recording geometry.
It does not include volume-Bragg selectivity, material shrinkage, emulsion thickness, or polarization-dependent recording efficiency.
Those effects matter in more advanced holography, but the fringe-spacing equation already captures the core interference physics.
It is also helpful to remember the physical meaning of one fringe.
Moving from one bright fringe to the next corresponds to a phase change of \(2\pi\), which means the optical path difference changes by exactly one wavelength:
\[
\Delta(\text{path})=\lambda.
\]
So the hologram is essentially a very fine record of local phase relationships across the recording plate.
At a more advanced university level, holography is described in terms of wave vectors, diffraction efficiencies, coupled-wave theory, and volume holograms.
In volume holography, the grating thickness becomes important and the reconstruction can become highly angle- and wavelength-selective.
But for an introductory thin-hologram picture, the three central quantities remain
the recording wavelength,
the beam angle,
and the fringe spacing.
\[
d=\frac{\lambda}{2\sin(\theta/2)},
\qquad
\nu=\frac{1}{d},
\qquad
K=\frac{2\pi}{d}.
\]
These formulas let you estimate how fine the recorded interference pattern is and provide a first step toward understanding why holograms can later reconstruct realistic virtual or real three-dimensional images.
