Objective The wind field in the middle and upper atmosphere is a crucial parameter in the study of atmospheric dynamics. High-resolution and high-precision detection of the wind field can provide more comprehensive data support for further understanding the local or global atmospheric wave conditions, the coupling process between different altitudes of the atmosphere, and the characteristics of atmospheric material and energy transport. The wind imaging interferometry has become an effective means for detecting the wind field in the upper atmosphere. The representative instrument of the four-zone birefringent static wind imaging interferometry technology, the Birefringent Doppler Wind Imaging Interferometer (BIDWIN), has advantages such as good stability, small size, light weight, and low calibration difficulty. This paper aims to establish the Jones matrix model of BIDWIN, simulate and analyze the variation of the phase steps in the four-zone field of view, study the variation of the usable field of view range of BIDWIN with the optical misalignment of the system, provide guidance for the instrument development, calibration, maintenance, and wind field detection experiments, and optimize the development of the four-zone birefringent static wind imaging interferometry technology scheme.

Methods Based on the system principle of BIDWIN, the Jones matrix model of the instrument was established to elaborate the principle of wind field detection. A birefringent Doppler wind imaging interferometer optical system was designed, relevant parameters were set, and the Jones matrix model was used to simulate the four-zone interferogram obtained on the detector. The BIDWIN Jones matrix model was used to simulate the rotation and tilt of the second delay plate relative to the first delay plate, as well as the rotation of the entire field widened delay plates, and analyze the variation of the phase steps across the field of view in the case of optical misalignment of the instrument.

Results and Discussions The simulated four-zone interferogram showed that the interferogram was divided into four zones, and each zone still retained the annular feature. The phase steps of the four zones of the interferometer will change with the field of view and do not always satisfy the four-step full-cycle equidistant sampling. Among them, there must be 0° and 180° in the four phase steps (Fig.3). If the other two phases are also close to or equal to 0° and 180°, it will cause the condition number of the measurement matrix to be extremely large, resulting in a large measurement error of the wind speed. The parameter sin(Q) changed with the field of view, and two zero-value lines appeared in the field of view, indicating the existence of a maximum wind speed error. The usable field of view of the instrument was limited between the two red strips (Fig.5). When the crystal of the delay plate had a relative rotational misalignment, the usable field of view would become narrower, and with the increase of the rotation angle, the usable field of view would correspondingly narrow (Fig.6-Fig.7); when the delay plate had a tilt misalignment, the usable field of view would remain unchanged but would shift in the overall field of view (Fig.9-Fig.10). If the area with a large wind speed measurement error in the center of the field of view was excluded, a larger available field of view can be obtained, comparing with the situation where the optical system is ideally aligned; when the entire instrument was deflected, the area with a large wind speed measurement error would be slightly curved, but the actual usable field of view would remain basically unchanged (Fig.12).

Conclusions Simulation results show that because BIDWIN uses a Wollaston prism to angle-shear the beam before the field widened delay plates, the phase steps of the upper and lower zones vary greatly in the vertical direction of the field of view, creating mathematically underdetermined and therefore unmeasurable wind speed strips at specific locations, which limit the usable field of view of the instrument. When the relative rotation misalignment of the crystal slabs occurs, the angle of rotation increases, resulting in a narrowing of the distance between the two strips, an increase in the number of strips in the field of view. If it is required to maintain more than 80% of the field of view in the ideal case, the rotation misalignment angle should be within ±0.2°. When there is a tilt misalignment in the delay plate, the usable field of view remains the same but shifts in the overall field of view. If the required field of view displacement is no more than 4 image elements, the tilt misalignment angle should be within ±0.03°. If the instrument is deflected as a whole, the strips will be slightly curved, but the actual usable field of view range will be essentially unchanged.