A spatial light modulator (SLM) is a digital device that quantitatively modulates light phase information. Ideally, the phase shift is linearly proportional to the grayscale, which is loaded into the SLM. However, the SLM grayscale is not linear with respect to the modulation voltage. In addition, when the incident wavelength is inconsistent with the working wavelength, the phase shift changes under the same grayscale. Therefore, the SLM must be calibrated before use. The traditional phase calibration of SLM is mainly realized through double-slit interference fringes, where the phase shift depends on the shift in the interference fringes. Unfortunately, owing to environmental vibrations, traditional phase calibration methods do not have adequate precision. To improve the measurement precision of the SLM phase calibration, even with environmental vibration, a self-reference interference method with Meslin-split photon sieves is proposed to compensate for system perturbation.

Meslin-split photon sieves with two different focal lengths are fabricated on the same chrome. The optical detector is located in the middle of the two focal planes, and it records the interference fringes. In the experiment, a laser is used as the light source, which is collimated and expanded after a deflector, and divided into two paths using a beam splitter. One light beam reaches the SLM, where it is loaded with grayscale and reflected back to the beam splitter, and then passes through the Mesin-split photon sieves. However, owing to the influence of system jitter and other factors in the experiment, the interference spot results in a displacement error. The absolute coordinate origin of the measurement system is introduced to improve the measurement accuracy and robustness of the optical system. After a simple calculation, the absolute displacement is converted into the displacement relative to the absolute coordinate origin, which effectively reduces the environmental perturbation. The corresponding interference fringes are recorded when the greyscale maps are sequentially loaded into the SLM. In this case, the shift distance between the interference fringe and the absolute coordinate origin is calculated, and the modulated phase shifts corresponding to different grayscale values are calculated. The phase shift as a function of the grayscale is obtained by fitting the measured greyscale to the phase relationship.

A common optical-path experimental scheme is used to calibrate the laser at 633 nm and 488 nm. Taking 633 nm laser illumination as an example, the grayscale is changed from 0 to 255, and the sampling interval is set 8. Thus, 32 frames of interference fringes are sequentially recorded. First, the absolute coordinate origin is calculated using the weighted centroid algorithm. The center coordinates of the interference fringes are calculated in the same manner. The center coordinates of the interference fringes are used to subtract the absolute coordinate origin and the shift of the interference fringes is obtained. The difference above is denoted by the baseline corresponding to the grayscale of zero. The differences corresponding to other grayscales are used to subtract the baseline, the absolute shifts of the interference fringes are successively obtained, and the environmental perturbation is completely eliminated. Finally, a grayscale-phase curve is obtained by linear fitting. The operation on the 488 nm laser illumination is the same as that on the 633 nm laser illumination. The variances of the fitted functions are 0.9967 and 0.9972 for the two wavelengths, respectively. As evidenced by the data, the closer the value is to 1, the better the obtained results. To verify the accuracy of the phase calibration of the SLM performed by the Meslin-split photon sieves, the Mesin-split photon sieves and charge coupled device are replaced by the wavefront sensor for phase measurement. For convenience, a super-Gaussian beam is used for the phase measurement. The experimental results show that the phase values of wavefront sensor agree well with the grayscale phase values obtained using our proposed self-reference interferometric method with Meslin-split photon sieves. The experimental results verify that the phase calibration of the SLM with Meslin-split photon sieves has high accuracy and good robustness.

This study presents a self-reference interferometric calibration method using Meslin-split photon sieves that is robust and easy to operate. The Meslin-split photon sieves form interferometric frings with a high signal-to-noise ratio in the middle of the two focal planes, while the absolute coordinate origin is generated by another independent photon sieve to make the calibration scheme less demanding in terms of optical path stability and detector sensitivity, as well as meet the requirements of SLM calibration in different environments. The grayscale-phase curve of the SLM calibration is verified by the wavefront sensor, which demonstrates that the photon sieves have high accuracy and stability for SLM interferometric calibration and are capable of meeting the accuracy requirements of different SLM applications.