Spaceborne infrared Fourier transform spectrometers are critical instruments in remote sensing and atmospheric observation, which offer high resolution, high throughput, and multi-channel capabilities to acquire high signal-to-noise ratio (SNR) spectral data. However, during the data acquisition process, the interferograms captured by these spectrometers are often affected by factors such as readout circuit noise, sampling delays, temperature variations in the interferometer, and inherent instrument characteristics. These influences result in deviations from the zero optical path difference (ZPD) position, which causes phase shifts that disrupt the symmetry of the interferogram. Such phase errors are particularly detrimental, as they can introduce significant radiometric calibration errors, compromise the accuracy of the data products retrieved, and adversely affect applications that rely on precise signal integrity, including atmospheric sounding, spectral analysis, and target detection. Conventional methods, such as the Forman and Mertz algorithms, struggle to balance accuracy and computational efficiency, particularly when addressing nonlinear phase errors or achieving sub-sampling-level correction.

To meet the demand for accurate and fast phase correction for spectrometers, we propose a phase correction algorithm, the minimum spectral imaginary part-simplex method (MSI-SM), which is based on the minimum spectral imaginary part method combined with the simplex algorithm. Through an analysis of the working principle of the Fourier transform spectrometer, the MSI-SM algorithm identifies the sources of phase error and decomposes the phase into linear and instrument phases. Target scene calibration is performed using blackbody and deep-space calibration sources during the spectrometer’s in-orbit operation, and the influence of instrument phase error is eliminated through the in-orbit calibration equation. In addition, we design an objective function for construction based on the minimum spectral imaginary part method, combined with the simplex algorithm to calculate linear phase errors and improve the computational efficiency and accuracy of the correction algorithm.

In the experiment, we select HIRAS data from March 1st, 3rd, 5th, and 7th, 2019, conducting tests at different times of the day and for various spectral band ranges. Artificial offsets are introduced at different positions in the interferogram to validate the algorithm, and traditional methods are employed for the evaluation and analysis of our approach. As shown in Fig. 10, the comparison of phase results relative to the internal calibration blackbody demonstrates that the proposed algorithm can accurately calculate sub-sampling-level phase errors. Furthermore, the experiments are repeated across longwave, midwave, and shortwave bands to verify the algorithm’s applicability. To quantitatively assess the correction accuracy, we refer to the noise equivalent delta radiance (NEDN) of deep space (DS) scene-calibrated spectra and the average NEDN across four field of views (FOVs). As shown in Fig. 11, compared to the instrument phase alignment (IPA) algorithm, the proposed method achieves NEDN values for the imaginary spectrum of the Earth scene (ES) and the real spectrum of DS calibration that are closer to the reference. Tables 4 and 5 indicate that MSI-SM outperforms the comparison methods on these metrics. Specifically, compared to the IPA algorithm, the proposed method shows superior performance in most cases, which improves the Average NEDN metric by 0.212%, 6.935%, and 22.38% for the three spectral bands, respectively. This improvement is primarily attributed to the limitations of the IPA algorithm. It relies on fitting residual phases and calculating phase offsets based on the slope of zero-intercept straight lines. This fitting process is highly dependent on the local characteristics of the data. If noise or outliers exist in the region, they may be mistakenly identified as signals during fitting, which leads to correction errors and significant deviations, especially in midwave and shortwave bands with lower signal-to-noise ratios. In contrast, the proposed method iteratively optimizes the objective function globally to find the optimal solution, avoiding reliance on the quality of single-band data. This effectively suppresses noise interference and results in more precise phase correction. To further illustrate the advantages of the proposed algorithm, we compare the efficiency of several correction methods used in the experiments. As shown in Table 7, the proposed method also significantly outperforms other traditional algorithms in terms of timeliness.

We propose a phase correction method for spaceborne infrared Fourier transform spectrometers based on the minimal spectral imaginary part approach and the simplex algorithm. Through comparisons with existing methods, the proposed approach demonstrates significant advantages in both correction accuracy and computational efficiency. During the on-orbit operation of Fourier transform spectrometers, phase errors among the three observation scenes introduce correlated noise into the imaginary part of the calibrated complex spectrum, thereby amplifying the spectral imaginary component. To address this issue, we analyze the sources of phase errors and eliminate those caused by instrument characteristics and internal radiative effects using an on-orbit calibration formula. The norm of the imaginary part of the calibrated spectrum is defined as the objective function, and the simplex algorithm is employed to leverage its strengths in solving linear function problems. This allows for the accurate and rapid calculation of linear phase deviations caused by sampling errors, which achieves sub-sampling-level precision. Finally, the proposed method is tested using interferometric data from the HIRAS onboard the Fengyun-3D satellite. Experimental results further validate the superiority of the algorithm in terms of both correction speed and accuracy. Compared to existing phase correction methods, the MSI-SM algorithm exhibits significantly better performance in NEdN metrics, thus providing robust technical support for improving the observational accuracy of spaceborne infrared Fourier transform spectrometers during on-orbit operations.