The cross term carries the missing relation
An ordinary photograph records intensity and generally loses the phase needed to propagate a complex object wave backward. Gabor’s method adds a known coherent reference during exposure. Their interference makes relative phase affect the recorded fringes.
Normalize the object and reference field amplitudes so that squared modulus gives intensity. The equation expands the recorded intensity into object and reference backgrounds plus two cross terms. An asterisk denotes complex conjugation. The terms encode a relative phase; they do not measure an absolute phase independent of the reference.
Sources: [2]
The first ambition was electron microscopy
Gabor developed wavefront reconstruction while seeking a route around electron-lens limitations. Early optical demonstrations used filtered conventional light. The 1971 lecture traces the later transformation brought by lasers and off-axis recording.
It is therefore inaccurate to require a laser for every historical realization of holography. Adequate spatial and temporal coherence, geometry and recording resolution are the physical requirements. A laser made many useful arrangements much more practical.
Reconstruction is a second physical step
After development, the recorded pattern modulates a reconstruction beam. In a simple linear thin-record approximation, multiplication by a matching reference can generate an object-wave term, along with a conjugate image and background. The viewer receives a wave with directional information, which can support parallax and refocusing.
The approximation assumes an appropriate recording response. Saturation, finite pixel or grain size, wavelength mismatch and mechanical motion can spoil the result. A decorative three-dimensional render does not demonstrate this recording-to-reconstruction chain.
Sources: [2]
The twin image explains a historical obstacle
In-line recording lets conjugate contributions overlap. Their simultaneous presence limits a straightforward interpretation of the reconstructed image. Off-axis reference geometry shifts terms into different angular or spatial-frequency regions so that suitable filtering can separate them.
Separation consumes recording bandwidth. A steeper reference angle needs finer fringes; finite sampling and numerical aperture constrain the field of view and resolution. Holography keeps phase information through interference, but does not remove those instrumental limits.
Sources: [2]
Keep the fringe record beside the reconstruction
Follow Gabor’s recording and reconstruction figures in pairs. In the linked studio, change the reference geometry and inspect both the stored interference and the reconstructed result. The explanatory test is whether the latter changes through the former, with sampling limits kept visible.
Sources: [2]