Correlation Efficiency = Energy in Correlation Peak (7.3)
 Energy Leaving Hologram


The term Horner efficiency was originally applied to that which is here

called the medium efficiency.28 More recently, the Horner efficiency

has been re-defined to describe the total efficiency including the

correlation efficiency due to diffraction.29 This new definition

seems to describe more accurately Horner's original intent that the

efficiency represent the entire correlation process including the

transparency and diffraction effects.


Total Efficiency = Energy in Correlation Peak (7.4)
 Energy in Test Image


The signal-to-noise and efficiency for the ideal auto-correlation of a

square are tabulated in Table 7.1 for cases where no pre-processing,

high-frequency emphasis, and phase-only filtering are applied.

 Simulation of a Continuous-Tone Hologram

 The ideal correlation is useful for understanding the various

pre-processing effects. In fact, for the on-axis hologram this ideal

correlation model accurately predicts the actual results. However,

holographic materials cannot record complex values, so off-axis

techniques are required. The spatial modulation or other mapping from

complex to real valued functions has a pronounced effect on the action

of the reference filter. This step must be included to reflect the

action of the hologram in an optical correlator. Figure 7.7 shows a

block diagram of the simulation of an optical correlator using a

continuous-tone hologram. Although quite similar to the ideal