Fig. 2.
Schematic illustration of structured illumination in k-space. a The imaged object has spectral components ranging from −km to km. b The Fourier transform of the pattern generated in ASI at the focal depth. The pattern has three non-zero components located at −k1, 0, k1. c Superposition of the pattern on the object in the spatial domain, translates into a convolution between their k-space components. Because of the frequency mixing, duplications of the original object occur. d On receive, the duplications of the original object in k-space are multiplied by the rectangular receive transfer that has a cutoff frequency of kc. As a result, the result in c is low-pass filtered; however, the product contains the high-resolution data downshifted due to the additional duplications. e Post processing includes the multiplication of the result by a second pattern, similar to the ideal transmitted pattern, generating additional duplications. Using a single image, the frequency components are not fully separated; thus, artifacts appear in the reconstructed image. f A precise reconstruction of the object is created by shifting the pattern, multiplying each captured image by a corresponding decoding pattern, and summing the product images. g The equivalent lateral transfer function of ASI is rectangular with a width ranging from -(kc + k1) to +(kc + k1)