Results and Discussions The experimental results show that the maximum phase modulation value of the LC-SLM at the standard light wavelength of 633 nm is 6.185 rad, which is close to the pre-calibrated phase modulation value of 2π. The relative error is 1.56%, less than the maximum phase fluctuation of 5% given by the manufacturer, indicating that the measurement accuracy of digital holography is high (Fig. 4). The repeatability error of digital holography is 1.34%, which is lower than 2.44% of Twyman-Green interferometry (Fig. 6). Compared with Twyman-Green interferometry, digital holography can measure the phase modulation characteristics through one digital image-plane hologram. Moreover, the measurement process will not be easily affected by the time fluctuation characteristics of the LC-SLM caused by external environmental change and unstable driving voltage. Therefore, digital holography has the advantages of high measurement accuracy and good real-time performance. Then, the inverse interpolation method is used to establish the look-up table (LUT) of the input gray level and the driving gray level, which effectively reduces the nonlinear error of the phase modulation characteristics from 6.5% to 2.45% (Fig. 7). Finally, the phase modulation characteristics of the LC-SLM at a non-standard light wavelength of 670 nm are recalibrated, and the maximum phase modulation value is 5.641 rad (Fig. 8). With the phase correction coefficient model built in this work, the actual correction coefficient of 670 nm relative to 633 nm is calculated to be 0.9121. The relative error between the actual correction coefficient and the theoretical correction coefficient is 3.46%, which is mainly caused by the phase modulation fluctuation error of the LC-SLM.

As a new type of phase modulator, the liquid-crystal spatial light modulator (LC-SLM) has been widely used in adaptive optics, optical communication, optical tweezers, and digital holography. However, the phase modulation characteristics of LC-SLMs are different generally, and the accuracy of phase modulation will be affected by their transportation processes and application environments. Therefore, it is essential to measure and calibrate the phase modulation characteristics of an LC-SLM before using the device for phase modulation and compensation. Nevertheless, the currently used measurement methods still suffer from limitations. Traditional radial shearing interferometry and Twyman-Green interferometry are usually inefficient and difficult to meet the requirements for rapid detection. Commercial Fizeau interferometers can only measure the phase modulation characteristics of the LC-SLM at a fixed light wavelength. In addition, these methods ignore the influence of light wavelength on phase modulation characteristics. In this study, a fast measurement and calibration method based on digital holography is proposed, and the phase modulation characteristics of the LC-SLM at different light wavelengths are systematically evaluated. Digital holography exhibits excellent measurement accuracy and efficiency. We expect that our method can be helpful in improving the accuracy of LC-SLMs in phase modulation and compensation.

Digital holography is used to measure and calibrate an LC-SLM in this study. First, an experiment setup of a digital holography system is developed, in which the LC-SLM is used as an object. Then, a driving image with gray levels of 0-255 is loaded on the LC-SLM, and a digital hologram is recorded on the image plane. The phase distribution of the object wave can be obtained by using the reconstruction algorithm, and the relationship between the phase and the gray level of the LC-SLM at the specific wavelength can be determined. Next, without changing the structure of the setup, a comparative experiment is carried out using Twyman-Green interferometry, which requires 52 interference images to obtain the phase modulation characteristics. Afterwards, the inverse interpolation method is used to linearly correct the phase modulation curve and improve the driving accuracy of the LC-SLM. Finally, the formula of the phase correction coefficient at the specific wavelength is theoretically derived and experimentally verified by recalibrating the phase modulation characteristics at a non-standard light wavelength.

In this study, a fast measurement method based on digital holography is proposed to calibrate LC-SLMs. With this method, the phase modulation characteristics at a specific wavelength can be measured in real time by using only one digital image-plane hologram. This method improves the measurement efficiency thanks to the simple system structure and no need for diffraction propagation calculation. Without changing the structure of the setup, a comparative experiment which uses Twyman-Green interferometry is carried out to verify that digital holography has higher measurement accuracy. The experimental results show that the phase modulation range of the LC-SLM is 0-6.185 rad at the standard light wavelength of 633 nm, and the nonlinear error of the phase modulation characteristics is reduced to 2.45% by the inverse interpolation method, which effectively improves the linear driving accuracy of the device. Depending on the wavelength response characteristics of the LC-SLM, a phase correction coefficient model at the specific wavelength is built, and the actual phase modulation range of the LC-SLM at a non-standard light wavelength of 670 nm is corrected. This study verifies the feasibility of using an LC-SLM for phase correction in dual-wavelength interference measurement systems.