Based on the properties of the dove prism and the Fourier optics approach, the coordinate relationships among four spatial light modulator (SLM) sections in a vectorial optical field generator are derived and experimentally verified. Taking the coordinate system of the first SLM section as a reference, the coordinate displacements between the first section and subsequent sections are determined via employing specially designed four-quadrant patterns, which enable the visualization of the degree of freedom controlled by each SLM section. A complex optical field could be accurately generated through combining the derived coordinate relationships and pre-compensation of the measured coordinate displacements. Several typical complex optical fields are experimentally generated to demonstrate the validity of the proposed transverse alignment method.
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