Micromotion represents the characteristic motion arising from the interaction between a moving target and its surrounding environment, with typical examples including nutation and precession [1], [2], [3], [4]. The single-pixel target velocity detection system is adept at capturing this new dimension of target features. In detection scenarios characterized by long distances and small sizes of targets, the application potential of such target micromotion feature detection is immense, whereas traditional target image features struggle to meet the demands of these contexts [5], [6], [7], [8], [9], [10]. The laser heterodyne detection system is capable of accurately acquiring information about target micromotion features [11], [12], [13]. However, the micromotion of the target introduces substantial random phase noise into the target echo. This random phase noise severely constrains the signal-to-noise ratio (SNR) of conventional laser heterodyne systems, ultimately interfering with their ability to detect target micromotion features.

A Photon Heterodyne Detection (PHD) method can overcome the limitations of phase noise on the traditional laser heterodyne SNR [14], [15]. By leveraging a unique photon pulse time interval detection technique, this method effectively mitigates the accumulation of random phase noise, thereby enhancing the SNR for micromotion target detection. Nevertheless, directly applying traditional spectrum-decomposition-based time–frequency analysis methods to PHD for extracting target micromotion features poses challenges. Specifically, the dispersion of echo energy in the frequency spectrum caused by micromotion restricts the concurrent improvement of SNR and time resolution in time–frequency analysis. Consequently, detecting high-frequency micromotion features becomes particularly arduous [16], especially when dealing with weak echoes at the photon level. Therefore, there is an urgent need to devise a novel method tailored for PHD that can efficiently extract target micromotion features.

In this work we proposes a novel Micromotion Modal Decomposition (MMD) method, which is suitable for photon heterodyne detection and can accurately extract target micromotion feature information carried by weak echoes at the photon level. Based on the operational mechanism of the MMD method, the energy of the target echo can be effectively accumulated on its highly fitting micromotion mode, thereby enhancing the SNR. This method can eliminate the dispersion of the echo energy in the spectrum caused by target micromotion, which decreases the SNR and limits the detection accuracy in traditional spectrum decomposition methods. The advantages of the MMD method are,

(1) In the case of photon-level weak echo (9×10−15W), the MMD method can achieve millimeter-level micromotion amplitude detection accuracy. Compared with traditional time–frequency analysis methods based on spectral decomposition, MMD allows for the detection of higher-frequency micromotion features, which helps capture the micromotion features generated by high-frequency motor driving systems.

(2) The MMD method can accurately identify multiple targets exhibiting different micromotion features within the detection field of view. This is of great significance for the detection and recognition of multiple targets.

(3) The MMD method can detect targets undergoing combined translational and vibrational motion by introducing target translational velocity parameters.