A ground⁃based infrared radiation characteristic measurement system not only undertakes the measurement of radiation characteristic, but also realizes the imaging in outfield. However, as for the manufacturing defects of the infrared focal the existing plane and the thermal radiation of system, it leads to the phenomenon of non⁃uniformity. Considering that the limitations of traditional non⁃uniformity correction algorithms, a variable integration time non⁃uniformity correction algorithm based on calibration was proposed in this paper. To confirm the effect of the proposed algorithm，the verification experiment based on 600 mm aperture mid⁃infrared radiation measurement system. The experimental results show that the original image non⁃uniformity under 2.5 ms and 3.0 ms is reduced from 3.69% to 0.22%. It is confirmed that the proposed algorithm has good correction effect and has engineering application significance.

It is important to search for new integrable equations hierarchies in soliton theory. First, a new equations hierarchy was constructed. Taking use of higherdimension Lie algebra A2 and the corresponding loop algebra [AKA~]2, it was proved that the equations hierarchy is Lax integrable. Then, the biHamiltonian structures of the Lax integrable hierarchy were constructed by making use of the trace identity. Finally, the infinitely conserved densities for the equations hierarchy was obtained and it was proved that the Lax equations hierarchy is Liouville integrable.