The cross terms keep the phase relative to the reference
An ordinary photograph records intensity and generally loses the phase needed to trace the object wave backward. Gabor added a known coherent reference wave during exposure. The two waves interfere, so their relative phase shapes the recorded fringes.
Scale the object and reference fields so that the squared modulus of each gives an intensity. The equation then splits the recorded intensity into two background terms, one from the object and one from the reference, plus two cross terms; the asterisk marks the complex conjugate. The cross terms hold the phase relative to the reference, not an absolute phase.
Sources: [2]
Gabor first aimed at the electron microscope
Gabor developed wavefront reconstruction while looking for a way around the limits of electron lenses. The early optical demonstrations used filtered light from conventional sources. The 1971 lecture then follows the change that lasers and off-axis recording brought later.
Holography therefore does not strictly need a laser. Its physical requirements are enough spatial and temporal coherence, a suitable geometry and enough recording resolution. Lasers made many useful arrangements far more practical.
Reconstruction is a second optical step
Once developed, the recorded pattern modulates a reconstruction beam. If the hologram is thin and responds linearly, illuminating it with a beam that matches the reference can produce the object wave, together with a conjugate image and a background. The viewer then receives a wave that carries direction, which can allow parallax and refocusing.
That approximation assumes a suitable recording response. Saturation, finite pixel or grain size, a wavelength mismatch and mechanical motion can all spoil the result.
Sources: [2]
The twin image was an early obstacle
When the reference runs along the same axis as the object wave, the image and its conjugate overlap, and the reconstruction is hard to interpret directly. Tilting the reference off axis moves the terms into different angles or spatial-frequency bands, where suitable filtering can separate them.
That separation costs recording bandwidth. A steeper reference angle means finer fringes, and finite sampling and numerical aperture limit the field of view and resolution. Interference lets holography keep phase information, but it does not lift these instrument limits.
Sources: [2]
Four lenses can fool a camera without keeping the phase
A camera works like the plate in the first section: it records how much light lands at each point of its image. Which point of a scene appears where depends only on the height and direction of each ray entering the lens. In 2014 Joseph Choi and John Howell of the University of Rochester used this to build a cloak from four ordinary lenses. With the right focal lengths and spacings, every ray near the axis leaves the last lens at the height and in the direction it would have had after crossing the same length of empty air.
Between the lenses, the light that will reach the camera squeezes into a narrower bundle along the axis. An object in the ring around that bundle blocks none of it, so it leaves no trace in the picture. With a camera 3.1 m in front, zoomed in on a gridded wall 1.9 m behind, the grid seen through the lenses matched the wall around them while part of a ruler inside disappeared. The axis itself must stay clear, the viewing angle must stay small, and the edges of the lenses still show.
Choi and Howell said plainly that they kept to ray optics and did not try to preserve the phase of the light. A perfect cloak would restore the whole field, amplitude and phase, so that no measurement could find a change. Theirs is built for instruments that record where light lands and how bright it is. Their demonstrations were camera images. A hologram records exactly what the design leaves aside: phase relative to a reference.
Sources: [3]
Look at the fringes and the reconstruction together
Read Gabor’s recording and reconstruction figures in pairs. In the linked studio, change the reference geometry and look at both the recorded fringes and the reconstruction. The test is whether each change in the reconstruction can be traced to a change in the fringes, with the sampling limits in view.
Sources: [2]