Fig. 1. Schematic diagram of pixel aliasing and square aperture. (a) Image acquisition function; (b) image spectrum; (c) case of Nyquist sampling theorem satisfied; (d) case of Nyquist sampling theorem unsatisfied; (e) planform of frequency domain of acquired image in case (d)

Fig. 2. Schematic diagram of structured illumination microscopy mounted with a square aperture

Fig. 3. Actual frequency domain distribution of structured light fringe information

Fig. 4. Square aperture design and physical drawing. (a) Collected frequency domain information of image when square aperture not added; (b) physical drawing of square aperture designed according to (a)

Fig. 5. Schematic diagram illustrating algorithm for frequency domain recovery

Fig. 6. Simulated data plot results of using spectrum recovery algorithm after occurrence of pixel aliasing. (a1) Wide-field data image; (a2) pixel aliasing image; (a3) pixel aliasing spectrum reconstruction image; (a4) ground truth image; (b1)‒(b4) locally enlarged images; (c1)‒(c3) frequency domain corresponding to (a1)‒(a4)

Fig. 7. Results of simulation data are obtained by using square aperture of different sizes. (a1) Reconstructed result after using a square aperture larger than calculated size; (a2) reconstructed result after using a square aperture smaller than calculated size; (a3) true data; (b1)‒(b3) locally enlarged images; (c1)‒(c3) frequencies corresponding to (a1)‒(a3)

Fig. 8. Schematic of images acquired by structured illumination microscopy system under different objectives. (a) 60×; (b) 100×

Fig. 9. Experimental setup diagram of square aperture structured illumination microscopy

Fig. 10. Square aperture frequency domain verification plot. (a1)‒(a3) Actual collected images under different patterns; (b1)‒(b3) frequency domain information without square aperture; (c1)‒(c3) frequency domain information with square aperture

Fig. 11. Results of wide-field image, pixel aliased reconstructed images, and reconstructed images with restored pixel aliased results in time and frequency domains. (a1)‒(a3) Images of time domains; (b1)‒(b3) locally enlarged images; (c1)‒(c3) frequency domain information; (d) box diagram of FWHM at each position in (a2) and (a3); (e) light intensity distribution