is compared to the spectral energy in the distorted energy. The
logical test input is a sine wave because it has a simple spectrum.
This technique for testing non-linearity is a long accepted method for
electrical systems. The output power when the sinusoidal spectral
components are removed, divided by the input power, is called the total
harmonic distortion (THD).
Amplifiers for speech and music are typically rated by their THD
specification. To measure THD in an audio amplifier, a sine wave is
input to the amplifier but is filtered from the output. Any remaining
power not at the input frequency is considered a result of harmonic
distortion. Applied to the analysis of film, a sinusoid input is
written to the film using the expression
s(x,y) = ( 1 + cos kx )/2 (6.13)
where k determines the spatial frequency. Note that the expression is
biased and scaled to provide an input between zero and one. This is
further scaled to utilize the entire dynamic range of the film. The
Fourier transform of equation 6.13 is
S(u,v) = 1/2 + 1/4 (u-k) + 1/4 6(u+k), (6.14)
and the power spectral density is
I(u,v) = 1/4 + 1/16 6 (u-k) + 1/16 S(u+k). (6.15)
There is a constant term and two spectral terms. The spectral terms
in the intensity image are down from the constant term by 1/4. Now
that the input spectrum is known, the film distortion is applied to
the input and the effect on the output spectrum is analyzed. The
sinusoidal input is shown in Figure 6.12. The film distorts the
sinusoidal input and transmits the pattern shown in Figure 6.13. The
spectrum of the distorted pattern recorded on the Agfa 8E75 plate is