# Integrated Optical Phased Arrays for Beam Forming and Steering
## 7 Performances
### Calibration  
Since OPAs operating at short wavelengths, performance monitoring and calibration are essential due to potentially significant pattern changes produced by slightly unavoidable processing imperfections [86]. Optical crosstalk deteriorates and even destroys patterns of OPAs. In addition, phase modulations, wavelengths of semiconductor lasers, and effective indexes are sensitive to temperature drift [73]. Thermal crosstalk and diffusions lead to performance degradations and errors due to the temperature dependence of steering angles, sidelobe suppression, and beamwidths. The effect of a temperature drift on the performance of OPAs should be considered [16]. Furthermore, electrical drifts are also universal in driving circuits. To correct phase errors and achieve designed far-field patterns, OPAs should be calibrated [40; 72; 102; 107]. Independently controlled OPAs enable phase calibration to mitigate fabrication errors, crosstalk, thermal and electrical drifts [45; 92; 96; 142; 145; 146]. For some OPAs, cascaded phase shifters are grouped to achieve fine tuning of the beam to compensate for any phase noise due to fabrication errors [106].  
In principle, OPA calibration requires measuring relative amplitudes and phases of all elements and compensating for mismatches [142]. Intensity has much less effect than phases on overall beamforming [146]. After measuring far-field patterns and discerning relative phases, an OPA was calibrated by iterative adjusting variable phase shifters [92]. A calibration with directly extracted phase differences from interference fringes was used to align random phases of another OPA [145]. Additionally, a look-up-table was used to calibrate element phase distributions of an OPA to achieve flexible 2D beam pointing within an FOV [11].  
OPAs with fabrication imperfections have undesired steering angles and usually require time-consuming calibration before practical uses. Some calibrations have been applied for different cases [69; 96; 146; 147; 148; 149]. Phase errors and background peaks of an OPA were minimized by feedback from a real-time far-field images infrared camera using a brute-force hill-climber optimization [96]. A phase modulation based on gradient ascent algorithm could also be used to calibrate OPAs [69]. A fast OPA calibration technique based on a stochastic parallel gradient descent algorithm (SPGDA) achieved the same quality images with random phase modulations. The SPGDA was three times faster than calibration used in a raster scanning scheme. Additionally, the SPGDA removed blurring and improved beam quality [147]. A chaotic stochastic parallel gradient descent algorithm combining chaos theory and SPGDA achieved fast adaptive phase correction with improved accuracy [148]. The SPGDA converged slowly and was easily stick to a local minimum. A deterministic stochastic gradient descent algorithm provided a rapid on-chip calibration, which was scalable to OPAs with flexible channel counts. In this way, chip sizes and complexities of OPAs were significantly reduced [149]. Mature optimizations, such as hill-climbing, stochastic gradient descent algorithm, genetic algorithm, particle swarm optimization, generally provide good calibration. However, such approaches are not well scalable and generally suffer from local extremum uncertainty. They are severe issues for OPAs with element spacing larger than a wavelength. A modified rotating element electric field vector approach was used to calibrate the initial condition of an OPA [146]. The approach follows a sequential individual antenna phase calibration process. A calibration result with more accuracy and predictability was achieved [146].