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The moiré fringe signal quality decides the precision of the encoder. In the production process of
RESR, usually, the moiré fringe signal quality is detected by the Lissajou graphs observing by the
oscilloscope. Lissajou graph is the common method for analyzing the dc level of two analog signals, the
amplitude of alternating current, the phase of signal, the relation of frequencies and other parameters. It is
convenient, intuitive, and would not be affected by the rate; furthermore, it applies to be used for field
detection. The ideal moiré fringe signal has two sine signals which phase difference is 90°, and prefect round
Lissajou graph. However, in practice, for a variety of factors, moiré fringe photoelectric signal has dc level,
higher harmonic, orthogonality deviation, equal amplitude deviation, and so on; that is why Lissajou graph will
appear offset or distortion. So we can observe the shape's deviation of the Lissajou graph in order to judge the
signal deviations. This paper introduces the diameter deviation to describe deviation between the Lissajou
graph of actual signal and the Lissajou graph of ideal signal, establishes the mathematical model of diameter
deviation, and theoretically analyzes the relationship between the diameter deviation and the parameters of
moiré fringe photoelectric signal. Using the VB6.0 simulation software to prove the results of the theoretical
analysis, we find that the simulation results agree with the previous detection, which supply theoretical
foundation for the observation of Lissajou graph. After analyzing the character of the encoder's signal when
the encoder works in a uniformly accelerated motion, we point out the applicative conditions of the observation
of Lissajou graph detecting moiré fringe signal. The conclusions of this paper have important significance for
detecting the signal quality of encoder, and have certain reference value for detecting other signals.
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