Single-snapshot multi-frequency demodulation in spatial frequency domain imaging enables real-time, accurate and wide-field optical property measurement of fruits

Spatial frequency domain imaging (SFDI) enables nondestructive, depth-resolved detection and is particularly well-suited for visualizing subsurface defects in fruits. However, traditional SFDI methods require multiple acquisitions to gather information at different frequencies and phases. In this study, we propose two novel single-snapshot multiple-frequency demodulation (SSMD) techniques that can simultaneously extract modulation transfer functions at multiple frequencies from a single image, thereby enabling multifrequency single-snapshot spatial frequency domain imaging. The first method is an SSMD approach based on an improved double Blackman window function. By optimizing the window function design, this method achieves an improvement in sidelobe suppression (reaching approximately −60 dB) while preserving the integrity of image edge structures. Experimental results demonstrate that the relative error in the reduced scattering coefficient (μ_s^') image is decreased from 21.22 % to 14.46 %, compared to the conventional method. The second method is the Frequency-Spatial Attention U-Net (FSA-Unet) deep neural network SSMD technique that integrates the Frequency-Spatial Attention mechanism. Evaluated using the normalized mean absolute error (NMAE), the frequency separation results of the FSA-Unet improve by 17.65 % and 16.18 % compared to the traditional U-Net. Moreover, this method reduces the relative error in the μ_s^' image to 5.98 %. These two methods are tailored for real-time monitoring of small samples and high-precision detection of large-scale samples, respectively. Experiments conducted on various fruits, including the apple, peach and pear, verify the adaptability and accuracy of the proposed methods under different detection requirements. The research findings provide a novel technical pathway for efficient, real-time, and multifrequency-integrated nondestructive quality assessment of fruits.