Expansion of phase uniqueness of projection methods when illuminated by sinusoidal pictures with different periods

Abstract

The article describes a method for eliminating phase ambiguity in the use of a series of measurements with different periods.
The choice of the period of sinusoidal patterns with given periods can be carried out using the structured illumination of the object. The phase information is obtained by the stepwise phase shift method. For this, three or more sinusoidal patterns with a given phase shift are projected onto the object. As a result of the decoding of the intensity patterns recorded, a field of phase quantities is obtained with a period determined by the magnitude of the period of the projected sinusoidal pattern. The same phase distribution can also be obtained with a different period. As a result of subtraction of phase pictures, the period of difference will be greater than the initial periods. The resulting period is determined by the equivalent period. The value of the equivalent period is inversely proportional to the difference of the initial periods. To increase the region of phase uniqueness, it is necessary to choose close periods. However, in this case, the error in determining the profile increases. The method proposed in the article obtains three or more series of sinusoidal pictures with different periods for illuminating the object. Reduction in error is provided by combining the phase values obtained for a minimum period with the values of phase transitions for the extended range, which allows to eliminate the effect of increasing the error and, accordingly, to reduce the overall phase error. Areas of phase transitions are automatically determined as a result of subtraction of the profile of the object obtained during measurements with different periods. Since the regions of phase transitions are homogeneous, we can propose a simple averaging procedure. Adding to the obtained field of phase transitions the measurement results with a minimum period, we obtain measurements with a minimum error. In this case, the periods of projected pictures do not need to be close. This choice of periods ensures the stability of the proposed method.