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