To meet the low polarization sensitivity requirements of space-borne multi-channel imaging spectrometers for atmospheric environment detection, and to overcome the shortcomings of traditional wedge crystal depolarizers which degrade instrument imaging quality, we design a multi-channel depolarizer based on the elasto-optical effect without causing image quality loss. The depolarizer overcomes the limitations of new liquid crystal and metasurface depolarizers such as narrow band range, low transmittance, and complex preparation. Based on existing research on photoelastic modulators, the complete theoretical analysis formula is derived for missile optical depolarizers, along with an examination of the influencing factors on the depolarizing effect and the optimal depolarizing conditions. To meet the multi-channel detection requirements of atmospheric environment detection imaging spectrometers, we propose a multi-channel depolarization method. This method uses the driving term to compensate for the delayed dispersion, which addresses the inherent wavelength dependence of the time-type photoelastic depolarizer and ensures that the residual polarization of each channel of the atmospheric detection imaging spectrometer is less than 2%.

In this paper, the complete theoretical calculation formula for the photoelastic depolarizer is derived from the Mueller matrix and the Stokes vector. The degree of polarization is analyzed with respect to key factors, such as the frequency of the photoelastic modulator, the peak delay, the polarization angle of the incident light, the integration time, and the angle between the optical axes of the two photoelastic modulators. The peak delay of the photoelastic modulator is 2.405 rad when the optimal depolarization is achieved. A method for compensating the delayed dispersion of the photoelastic modulator using the driving term is proposed, based on the relationship between the depolarization spectrum width, central wavelength, and residual polarization degree. This method can effectively overcome the inherent wavelength dependence of the photoelastic modulator, thereby enabling multi-channel simultaneous and efficient depolarization of the spaceborne atmospheric detection imaging spectrometer, which lays a theoretical foundation for improving the accuracy of atmospheric parameter inversion.

A single photoelastic modulator cannot effectively depolarize linearly polarized light in all directions. The dual photoelastic modulator structure can achieve omnidirectional depolarization, but the optical axes of the two modulators need to be placed at 45° to avoid the phenomenon where the residual degree of polarization oscillates with the integration time (Fig. 6). Theoretical calculations show that the best depolarization effect can be achieved under multiple peak delays. Selecting the first peak delay of 2.405 rad can minimize the peak-to-peak value of the driving voltage and reduce the difficulty of circuit design (Fig. 3). The peak delay of the photoelastic modulator is greatly affected by the driving circuit. Under the existing circuit stability conditions, a delay deviation of 0.01 rad will lead to a 0.5% decrease in depolarization (Table 2). The influence of incident light polarization angle and integration time is relatively small and easy to control. In this paper, the relationship is established between the depolarization spectrum width, center wavelength, and residual polarization degree. In addition, based on the establishment of this relationship, a method using the driving term to compensate for the delayed dispersion of the photoelastic modulator is proposed to achieve multi-channel depolarization of the photoelastic depolarizer. However, the maximum depolarization degree that each channel can achieve is limited by the channel bandwidth (Fig. 8). Therefore, it is necessary to divide channels with wide bandwidths into two or more segments for depolarization. Finally, we design a photoelastic depolarizer, which allows each channel of the four-channel imaging spectrometer to achieve a depolarization degree of more than 98% under the adjustment of the peak-to-peak value of the five driving voltages (Tables 3 and 4).

To solve the inherent limitations of traditional wedge crystal depolarizers and time-type depolarizers, we propose a method for realizing multi-channel depolarization by extending the theoretical formula for missile optical depolarizers and analyzing the influence of key parameters. The dual-elastic-optic modulator structure can effectively realize the depolarization of omnidirectional linearly polarized light, and selecting the first peak delay can reduce the difficulty of designing the driving circuit. A multi-channel depolarization technique is also proposed, which uses the driving term to compensate for delayed dispersion. By adjusting the five peak-to-peak voltage values to drive the photoelastic depolarizer, the depolarization degree of each channel in the four-channel spaceborne atmospheric detection imaging spectrometer can exceed 98%. The depolarizer offers advantages such as minimal image quality loss and autonomous switching between application channels, which makes it highly promising for future applications. Before practical implementation, however, it is necessary to consider the influence of environmental factors, calibration and installation errors, and driving circuit stability on the depolarizer’s performance, to enable the engineering application of the photoelastic depolarizer in spaceborne imaging spectrometers.