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