Different from traditional optical microscopy, computational microscopy does not rely on high numerical aperture objective lens. Common computational microscopes include structured illumination microscopes, microsphere lens optical microscopes, Fourier ptychographic microscopes and so on. However, single measurements from a computational microscope are usually not directly used for imaging. Computational microscopy needs a large amount of measurement data to recover a high-resolution target image, which is a method to exchange time resolution for space resolution. Traditional contrast focusing methods or phase detection methods are not suitable for computational optical microscope because they rely on high-quality image acquisition and analysis. At present, there are no reports on the general focusing method for computational microscope.
To address this problem, Professor Gong Xinglong and Professor Deng Huaxia of the University of Science and Technology of China proposed a grating-free single-pixel Fourier autofocus method. This method makes full use of the frequency-domain information acquisition ability of light field modulation and the out-of-focus mechanism of optical microscopy. By analyzing the spectrum energy distribution of the out-of-focus image, the focal plane of the microscope can be located quickly by the light intensity measurement sequence of a photodetector. This method shortens the time consumption of single focusing detection from second level to microsecond level. The relevant research results are published in Photonics Research, Volume 12, Issue 6, 2024. [Guan Wang, Huaxia Deng, Yu Cai, Mengchao Ma, Xiang Zhong, Xinglong Gong, "Grating-free autofocus for single-pixel microscopic imaging," Photonics Res. 12, 1313 (2024)]
This method does not require additional grating and objective lens to achieve focusing, and is inspired by the physical mechanism of defocusing (Fig. 1a). Microscopic defocusing can be characterized by a point spread function (PSF). The PSF is approximated equivalent to a Gaussian convolution kernel in image blurring algorithms for digital image processing. The Gaussian convolution kernel is used to filter the image at low frequencies and suppress the high frequency information (Fig. 1b). Thus, fast autofocus can be achieved by recovering the high frequency information. To verify the general applicability of the grating-free autofocus method of this work, experiments are performed here on biological samples (Fig. 1c). Taking advantage of the unique advantage of Fourier single-pixel microimaging, i.e., the frequency-domain measurement capability, the focusing plane can be quickly located by simply measuring the response curve of the eigenfrequency. In the measured data of focusing experiments, the peak of the curve corresponds to the focal plane.
The single-pixel computational optical microscopy focusing technique proposed in this work does not rely on high-resolution two-dimensional array devices, but makes full use of the temporal modulation to rapidly locate the focal plane from the one-dimensional time-measured signals of light-intensity response, achieving microsecond computational microscopy focusing. This technique provides a new focusing scheme for conventional optical microscopy as well.
Fig. 1 (a) PD, photodetector; T, target; O1, objective lens 1; LC, light screen; DLP, digital light processing projector. Grating is removed. (b) Physical mechanism of SPMI's defocus. Numerical simulations of PSF and corresponding OTF with σ=2. PSF is an image of the ideal dot source transmitted from an objective lens. The PSF is transformed into the OTF, representing the optics system's low-pass filter characteristic. The high-frequency amplitudes decrease as σ increases. The microscopic image is blurred due to this high-frequency band limit. (c) Experimental results for grating-free method. Objective: 4× (NA=0.1), 10× (NA=0.25), 20× (NA=0.4). The PD sampling rate, 1 MHz. The DLP projecting rate, 22.7 kHz.
For future optimization, one could consider designing liquid lens to instead of shifting objective lens mechanically in SPMI's autofocus. The grating-free autofocus speed could potentially be further enhanced if used in conjunction with three-step or two-step phase-shift algorithms. It is also possible to achieve invisible light autofocus by maximizing the Fourier coefficient without imaging. In addition, combined with the single-pixel phase contrast imaging technology, the proposed grating-free autofocus method is expected to be applied to transparent samples' fast autofocus by measuring only the Fourier amplitude.
