Abstract

The frequency recognition algorithm for multiple exposures (FRAME) is a spatial frequency multiplexing method that enables high-speed videography with high spatial resolution across a wide field of view and high temporal resolution up to femtoseconds. The criterion to design encoded illumination pulses is an essential factor that affects the sequence depth and reconstruction accuracy of FRAME but was not previously discussed. When the spatial frequency is exceeded, the fringes on digital imaging sensors can become distorted. To exploit the Fourier domain for FRAME with deep sequences and avoid fringe distortion, the maximum Fourier map for sequence arrangement was determined to be a diamond shape. The maximum axial frequency should be a quarter of the sampling frequency of digital imaging sensors. Based on this criterion, the performances of reconstructed frames were theoretically investigated by considering arrangement and filtering methods. To ensure optimal and uniform interframe quality, the frames near the zero frequency should be removed and optimized super-Gaussian filters should be employed. Experiments were conducted flexibly with a digital mirror device to generate illumination fringes. Following these suggestions, the movement of a water drip dropping on a water surface was captured with 20 and 38 frames with uniform interframe quality. The results prove the effectiveness of the proposed methods to improve the reconstruction accuracy and promote the development of FRAME with deep sequences.

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