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Spatiotemporal Joint Modulation Fourier Transform Interferometric Spectroscopic Imager – Sagnac System Principle and Interference Matrix Extraction
Background Introduction
In the fields of computational optical imaging and hyperspectral remote sensing, spatiotemporal joint modulation Fourier transform interferometric spectral imaging technology, with its advantages of high throughput, significant signal-to-noise ratio gain, and all-solid-state hardware without moving parts, has become an indispensable technical path for aerospace payloads and precision laboratory detection. As the most representative architecture in this field, the Sagnac triangular common-path interferometer utilizes its inherent vibration resistance and compact physical structure to achieve efficient coupling and high-fidelity acquisition of target 3D information on the detector image plane through a clever combination of lateral shearing mechanism and carrier push-broom motion. This paper will focus on the optical physics of push-broom systems, deeply analyze the generation mechanism and spatiotemporal mapping law of interferometric field data, and discuss in detail the discretization extraction process of the interferometric matrix, aiming to provide rigorous theoretical basis and technical support for improving the spectral reconstruction accuracy in complex remote sensing environments.
To translate these theoretical advantages into engineering practice, Large Aperture Static Interferometric Imaging Spectroscopy (LASIS) was developed. As a significant breakthrough from traditional spatial modulation interferometric imaging, LASIS consists of a front optical system, a Sagnac interferometer, an imaging mirror (Fourier transform mirror), a detector (FPA), and a data acquisition system, as illustrated in Figure 1. Its basic principle is the introduction of a transverse shearing beam splitter into the infinity imaging system. Its core evolution compared to traditional interferometers lies in the reconstruction of the field stop: a large-aperture window-type aperture replaces the traditional slit field stop at the back focal plane of the front optical system. This improvement not only reduces the size of subsequent optical components by utilizing the front system but also enables the system to form a two-dimensional image of the target on the image plane (FPA). This leap from "line" to "plane" significantly improves the system's light transmission and detection efficiency while laying a crucial structural foundation for subsequent spatiotemporal joint modulation.
Figure 1. Schematic diagram of the optical path of a large-aperture static interferometric imaging spectrometer(Image source: Chen Tieqiao. Research on Hyperspectral Reconstruction Method Based on Interferometric Imaging Mechanism and Error Characteristics)
In this architecture, the interference information originates from the transverse shearing d generated by the Sagnac interferometer. Each beam of light from the target, upon entering the interferometer, is sheared into two parallel coherent beams, which converge at the same point on the image sensor (FPA) via the imaging mirror, causing interference. At the image plane, the optical path difference Δ of the interference is determined by the shearing d, the focal length f of the imaging mirror, and the distance y from the interference point to the zero optical path difference point. Since the value of y corresponds to the field of view of the spectrometer in the shearing direction, the optical path difference generated at each point on the FPA surface is spatially constant. This results in a unique morphology in the single-frame image acquired by LASIS, where two-dimensional spatial information superimposed on one-dimensional interference fringes. Specifically, at the instant of sampling, as shown in Figure 2, the detector pixel response is actually the spatially modulated interference data corresponding to the field of view of the target.
Figure 2. Schematic diagram of one-dimensional interference fringes superimposed with two-dimensional spatial information from a single frame image.
Technical Principles
However, a single frame image only records the instantaneous response of the target under a specific optical path difference. To obtain a complete interferogram covering all sampling bands for each ground target point, continuous frame pushbroom imaging along the spectral dimension (i.e., the shearing direction) is necessary. During the carrier's movement, the same ground target point is captured by different pixels on the detector at different times, and these pixels, due to their different spatial positions, correspond to different optical path difference modulations. When the pushbroom reaches the maximum optical path difference sampling range, a set of interferometric sampling points arranged in a time-series manner is formed. Therefore, the raw LASIS image data needs to undergo rigorous rearrangement and extraction: in the time-series images of the pushbroom, for each pixel in the spatial dimension, its corresponding interferometric data in each frame is extracted sequentially along the spectral dimension. This process of "extracting" the point interferogram from the time series is the core data processing logic of the spatiotemporal joint modulation spectrometer, as shown in Figure 3.
Figure 3. Rearrangement and extraction of LASIS raw image data
Results Analysis
Based on this physical process, the system reconstructs and extracts a novel three-dimensional data cube—LAMIS (Large-aperture Multispectral Interferometric Stack)—by scanning and recombining the full-field-of-view pushbroom image sequence. Within the LAMIS data cube, the data structure is finely decoupled: its spatial layer is a clean scene image after numerical processing and removal of interference fringes, realistically reflecting the geometric distribution of the target, as shown in Figure 4; while the interference dimension records the point interference curves corresponding to each column of ground features, as shown in Figure 5, which illustrates a two-dimensional diagram of the interference curves for a column of ground features. This process of "extracting" the LAMIS cube from the original spatiotemporally coupled image achieves the digital separation of spatial and interference information.
Figure 4. Clean scene image after removing interference fringes.
Figure 5. Two-dimensional schematic diagram of the interference curve of a series of ground features.