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Holography principles, Slides von Technikfolgenabschätzung(TA) / Technikbewertung

Alpen-Adria-Universität KlagenfurtTechnikfolgenabschätzung(TA) / Technikbewertung

Holographic imaging from gabor to off axis technologies

Art: Slides

2025/2026

Hochgeladen am 25.01.2026

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6. HOLOGRAPHY.
6.1. Gabor’s (In-line) Holography.
• In 1948, Dennis Gabor introduced “A new microscopic principle,” which he
termed holography. The method records the entire field information (i.e.
amplitude and phase) not just the usual intensity. Initially Gabor proposed this
technique to “read” optically electron micrographs that suffered from severe
spherical aberrations. In 1971, Gabor was awarded the Nobel Prize in Physics
“for his invention and development of the holographic method”.
• Holography is a two-step process: 1) writing the hologram, recording on film the
amplitude and phase information, and 2) reading the hologram, by which the
hologram is illuminated with reference field similar to that in step 1.
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6. HOLOGRAPHY.

6 .1. Gabor’s (In-line) Holography.

  • In 1948, Dennis Gabor introduced “A new microscopic principle,” which he termed holography. The method records the entire field information (i.e. amplitude and phase) not just the usual intensity. Initially Gabor proposed this technique to “read” optically electron micrographs that suffered from severe spherical aberrations. In 1971, Gabor was awarded the Nobel Prize in Physics “for his invention and development of the holographic method”.
  • Holography is a two-step process: 1) writing the hologram, recording on film the amplitude and phase information, and 2) reading the hologram, by which the hologram is illuminated with reference field similar to that in step 1.
  • Gabor’s original setup for writing the hologram is described in Fig. 1.

Figure 1. In-line optical setup for writing Fresnel holograms.

  • Assuming a linear response to intensity associated with the photographic film, we find that its transmission function has the form t x y ( , (^) ) = a + bI (^) ( x y , ) , ( 0. 2 )
  • a and b are constants.
  • The hologram is now written and all the necessary information about the object is in the transmission function t.

Figure 2. Reading an in-line hologram.

  • Reading the hologram means illuminating the hologram as if it is a new object (Fig. 2).
  • The last two terms contain the complex field U 1 and its U 1 *. An observer positioned behind the hologram will see at position z behind the transparency an image that resembles the original object (field U 1 ).
  • Field U * indicates “backward” propagation, such that a second ( virtual) image is formed at a distance z in front of the film. If the observer focuses on the plane of the first (real) image, she/he will see an overlap between the in-focus image and the out-of-focus (“twin”) image due to propagation over a distance 2 z.
  • This overlap significantly degrades the signal to noise of the reconstruction and represents the main drawback of in-line holography. This is the reason why Gabor apparently abandoned holography by the mid 1950’s.
  • In-line holography is the process of recording the Fresnel diffraction pattern of the object onto a photosensitive film. The visualization is the reverse process by which the hologram is illuminated with a plane wave and the resulting field observed at the same Fresnel distance away.
  • The existence of the twin images in essence is due to the hologram being a real signal, the Fourier transform of which must be an even function, i.e. symmetric with respect to the film position. In the following section, we discuss the method that circumvented the obstacle posed by the twin image formation and turned holography into a main stream technique.
  • In his 1962 paper, Leith acknowledges Lohman’s contributions [ 4 ]:
  • “A discussion of various similar techniques for eliminating the twin image is given by Lohmann, Optica Acta (Paris) 3 , 97 (1956). These are likewise developed by use of a communication theory approach.”
  • Leith and Upatnieks’ pioneering paper on off-axis holography was titled “Reconstructed wavefronts and communication theory” [ 4 ], suggesting upfront the transition from describing holography as a visualization method to a way of transmitting information.
  • Like radio communication, off-axis holography essentially adds spatial modulation (i.e. carrier frequency ) to the optical field of interest. Interestingly, Gabor himself, like most electrical engineers at the time, was familiar with concepts of theory of communication and, in fact, published on the subject even before his 1948 holography paper [ 8 ].

Figure 3. Off-axis setup for writing a hologram; k 0 and kr are the wavevectors of the incident and reference fields.

  • The total field at the film plane is ( ) ( ) ( ) (^ )

r rx rz

t F r^ i F r i k^ x^ k^ z

U x y U x y U e U x y U e

  + 

k r ( 0. 5 )

  • krx = k 0 sin  and krz = k 0 cos .
  • The z-component of the reference wavevector produces a constant phase shift, krzz , which can be ignored. Thus the resulting transmission function associated with the hologram is proportional to the intensity, i.e. ( ) ( ) ( ) ( )

(^2 )

, rx^ , rx

F r F r ik^ x^ F r ik^ x

t x y U x y U U x y U e −^ ^ U x y U e

Figure 4. Reading the off-axis hologram.

  • The last term in Eq. 7 is modulated at a frequency 2 krx. Observing along this

direction gives access to U F *, which reconstructs the object field behind the film, due to the complex conjugation. This is the virtual image.

  • The two images are now observed along different directions, without obstructing each other. The first two terms in Eq. 7, the DC component, propagates along the direction of k r , which is also convenient. With the proper off-axis angle for writing/reading, the real image can be obtained unobstructed. In practice, the modulation frequency, (^) krx , has to be carefully chosen to ensure the desired resolution in the final reconstruction; it must satisfy the Nyquist theorem applied to this problem.

6 .3. Nonlinear (Real Time) Holography or Phase Conjugation.

  • Exploiting the nonlinear response of materials, the writing and reading steps of holography can be combined into one. This process has been termed phase conjugation and proposed as a way to correct imperfections (aberrations) in imaging systems. Review its principle.
  • Yariv showed that nonlinear four wave mixing can be interpreted as real time holography. The principle relies on the third order nonlinearity response of the material used as writing/reading medium.
  • If an object field, U 3 , is applied simultaneously, the nonlinear induced polarization can be written as ( ) (^) ( ) ( ) (^ ) ( )

3 1 2 3 3 3

4 1 2 3 3 1 2 3 * (^3 1 23) *

NL i t i t

P U U U e U U e

 

     

 − − +  − + 

k k k r k r

  • The field emerging from the material, U 4 , is the time-reversed version of U 3 , as

indicated by the complex conjugation ( U 3 *).

  • The efficiency of generating this phase conjugated field U 4 can be calculated from the nonlinear wave equation , which yields two complex differential equation for the fields U 3 and U 4. The time-reversed field U 4 can exceed in power the incident object field U 3 , by converting some of the pump power.
  • Phase conjugation or real time holography has been used for various applications during the past decade [ 12 ]. Recently, this concept has received renewed attention in the context of tissue scattering removal [ 13 ].