Once :the correlation image is obtained, an analysis program
evaluates the signal-to-noise ratio and the efficiency of the
correlation process. The signal-to-noise ratio is determined by the
average of the correlation peak with its nearest six neighbors divided
by the average of the entire correlation image.
Signal-to-Noise = Correlation Peak (7.1)
Correlation Plane Average
The efficiency is determined by dividing the energy in the correlation
peak by the energy in the input test image. This efficiency is always
less than or equal to 1 because the reference pattern is normalized
and can only attenuate the test image energy. In the case of the
phase-modulated reference, the efficiency can actually reach 1 if all
of the diffracted light reaches the correlation peak. In this case,
no attenuation occurs at each pixel but rather a phase shift occurs.
Total efficiency can be divided into two effects, medium
efficiency and correlation efficiency. The medium efficiency depends
on the attenuation by the reference pattern and can be computed by
dividing the total light out of the reference pattern by the input
energy.
Medium Efficiency = Energy Leaving Hologram (7.2)
Energy in Test Image
The medium efficiency goes to 1 for a phase-modulated hologram. The
correlation efficiency is the energy in the correlation spike divided
by the total energy output from the hologram. This efficiency term
depends on how much of the output light is diffracted to the
correlation spike rather than to other orders.