###### Abstract  
To obtain highly sensitive, accurate, fast, and repeatable measurements of waveplate parameters over an entire clear aperture, a novel measurement method using dual differential frequency photoelastic modulations is proposed. Simple polarimetry is conducted based on two photoelastic modulators, which operate at different frequencies. The fast-axis azimuth and retardance parameters of the waveplate are loaded into the modulation signals. Employing digital phase-locked technology, the fundamental and differential frequency harmonic terms are extracted, and then the two parameters of the waveplate are demodulated. The principle is analyzed, and the measurement system is built for verification experiments. The experimental results reveal that the two parameters of the waveplate are simultaneously measured over the entire clear aperture. The standard deviations of the fast-axis azimuth and retardance are 0.02\({}^{\circ}\) and 0.03 nm, respectively, and the maximum relative deviations of the fast-axis azimuth and retardance are 0.6% and 0.06%, respectively. The single-point data measurement time is only 200 ms. The proposed method exhibits high precision and speed, and provides an effective quality inspection and calibration method for waveplates. waveplate; photoelastic modulation; differential frequency modulation; fast-axis azimuth; retardance +
Footnote †: journal: Applied  
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Footnote †: journal: Applied  
1  
modulation techniques. In the light intensity method, the waveplate is placed between two orthogonal polarizers, the light intensity is obtained at different angles by rotating the waveplate, and the retardance of the waveplate is calculated [6]. The polarization compensation method is based on the Senarmont compensation principle [7]. In accordance with the light intensity method, a compensator with a known retardance is added between the waveplate and the analyzer. Waveplate measurement is realized by observing the polarization angle produced by rotating the compensator or analyzer. Light intensity and polarization compensation methods have the advantages of a simple instrument structure and low cost. However, these two methods require the mechanical rotation of the sample and multiple measurements at different angles to measure the waveplate parameters. The measurement accuracy is limited, and the requisite multiple measurements are time-consuming, making them unsuitable for rapid measurement. Michelson interferometry or Mach-Zehnder interferometry is used to insert the waveplate into the measurement optical path [8]. The retardance of the waveplate can be calculated according to the optical path difference between the measurement and reference optical paths. This method has high measurement accuracy. Nevertheless, it is easily disturbed by environmental factors, such as temperature and environmental vibrations. Meanwhile, the laser feedback method incorporates the waveplate to be tested in the laser feedback cavity [9]. The length of the feedback cavity is scanned by a piezoelectric ceramic-driven mirror, and the polarization jump of the laser output light intensity is detected to realize the waveplate retardance measurement. The sample needs to be coated with a narrowband filter film for single-laser mode wavelengths. The measurement accuracy depends on the light intensity stability, and the measurement accuracy and repeatability are affected by the ambient temperature and vibration. Polarization modulation methods, such as electro-optic modulation, magneto-optical modulation, and photoelastic modulation, are used to measure the waveplate parameters [10]. Polarization modulation methods realize the modulation of light intensity, and alternating current (AC) light intensity signals are achieved. The waveplate parameters are loaded into the AC signals, and the measurements are completed by utilizing the change in the AC signal amplitude. The signal-to-noise ratio is thereby improved, and a more precise measurement is achieved.