Even after the Heydemann correction, residual nonlinear errors, ranging from hundreds of picometers to several nanometers, are still found in heterodyne laser interferometers. This is a crucial factor impeding the realization of picometer level metrology, but its source and mechanism have barely been investigated. To study this problem, a novel nonlinear model based on optical mixing and coupling with ghost reflection is proposed and then verified by experiments. After intense investigation of this new model’s influence, results indicate that new additional high-order and negative-order nonlinear harmonics, arising from ghost reflection and its coupling with optical mixing, have only a negligible contribution to the overall nonlinear error. In real applications, any effect on the Lissajous trajectory might be invisible due to the small ghost reflectance. However, even a tiny ghost reflection can significantly worsen the effectiveness of the Heydemann correction, or even make this correction completely ineffective, i.e., compensation makes the error larger rather than smaller. Moreover, the residual nonlinear error after correction is dominated only by ghost reflectance.

We investigated the influence of altitude on aero-optic imaging quality degradation of the hemispherical optical dome. Boundary conditions for the aerodynamic heating effect of the optical dome were calculated by solving the Reynolds-averaged Navier–Stokes equations provided by FLUENT. The finite element model and the thermal-structure simulation results of the optical dome were obtained using ANSYS. The 3D nonuniform refractive index field of the optical dome was obtained according to the thermal-optical effect. The optical tracking method based on the fourth-order Runge–Kutta algorithm was adopted to simulate the optical transmission through the optical dome. The Strehl ratio (SR), encircled energy, distorted target images, and peak signal-to-noise ratio were presented for imaging quality evaluation. The variation rules of these imaging quality evaluation parameters were obtained in the altitude range of 0–45 km. The results showed that, in the same flight conditions, with the increase of altitude, peak signal-to-noise ratio (PSNR) of the distorted image, and SR result were increased, and radiuses of dispersion spots, including 80% energy, were decreased; therefore, the influence of aero-optics effect on imaging quality degradation was gradually weakened.

We investigated the influences exerted by the nonuniform aerodynamic flow field surrounding the optical window on the imaging quality degradation of an airborne optical system. The density distribution of flow fields around three typical optical windows, including a spherical window, an ellipsoidal window, and a paraboloidal window, were calculated by adopting the Reynolds-averaged Navier–Stokes equations with the Spalart–Allmaras model provided by FLUENT. The fourth-order Runge–Kutta algorithm based ray-tracing program was used to simulate the optical transmission through the aerodynamic flow field. Four kinds of imaging quality evaluation parameters were presented: wave aberration of the entrance pupil, point spread function, encircled energy, and modulation transfer function. The results show that the imaging quality of the airborne optical system was affected by the shape of the optical window and angle of attack of the aircraft.

Distributed optical fiber strain sensing significantly increases the number of sensing points compared with FBG sensor, which makes it an excellent candidate for shape sensing. Theoretical analysis indicates that the spatial resolution of strain measurement is crucial to the performance of shape sensing, so a shape sensor based on differential pulse-width-pair Brillouin optical time-domain analysis (DPP-BOTDA) is proposed to improve the spatial resolution and shape sensing performance. The sensing fiber is attached on the both sides of a steel strip substrate, which enables the measurement of Brillouin frequency shifts (BFSs) of both the sides to suppress temperature crosstalk. In experiment, firstly, the dependence of BFS variation on the curvature of fiber is measured, the result of which agrees well with theory. Then the reconstruction of three shapes are demonstrated, the spatial resolution of which is 10 cm.

Grating interferometers that measure in-plane and out-of-plane displacements are not only effective two-degree-of-freedom (DOF) sensors, but are also basic units of six-DOF measurement systems. Besides resolution and accuracy, periodic nonlinear errors, misalignment tolerance, and size of reading heads are more crucial than ever. In this work, a spatially separated heterodyne grating interferometer that measures in- and out-of-plane displacements is proposed. A prototype with 3 mm diameter beams with a size of 69 mm × 51 mm × 41 mm was built and tested. The experiment results show that the 30 s stability is 2.5 nm; the periodic nonlinear errors of the two measuring directions are less than the resolutions (0.25 nm for in-plane motions and 0.15 nm for out-of-plane motions). Double-diffracted configuration ensures that the misalignment tolerances are three axes larger than ±2 mrad.

A conformal dome optical system was established and aberration characteristics of the dome were investigated using Zernike aberration theory. The conformal dome was designed with gradient index element. The designing method was introduced and the optimizing results were analyzed in detail. The results show that the Zernike aberrations produced by the conformal dome decreased dramatically. Also, a complete conformal optical system was designed to further illustrate the aberration correction effect of gradient index elements. The results show that the utilization of gradient index optical elements not only improves the imaging quality, but also simplifies the structure of the conformal optical system.