A method to produce an enhanced resolution image from images of a target captured under structured illumination, the method including: transforming at least three images of the target (1811, 1813, 1815), captured by a sensor in a spatial domain, from at least three phase displacements of the structured illumination along one angle, into a Fourier domain to produce at least three frequency domain matrices, wherein each matrix of the at least three frequency domain matrices comprises a first block of complex coefficients and a redundant, second block of complex coefficients, wherein each complex coefficient of the second block of complex coefficients is a complex conjugate of a respective complex coefficient of the first block of complex coefficients; using estimated reconstruction parameters, applying an inverse mixing matrix to the first blocks to produce at least three phase-separated half-matrices in the Fourier domain, which are an unshifted half-matrix and shifted half-matrices; performing one or more intermediate transformations on the phase-separated half-matrices, including: subpixel shifting, by transforming from the Fourier domain into the spatial domain the shifted half-matrices, applying a multiplication to data in the spatial domain to generate translated data, and transforming the translated data from the spatial domain data back into the Fourier domain to produce realigned shifted half-matrices; and calculating complex coefficients of second blocks in the Fourier domain to produce full matrices from the half-matrices, after the intermediate transformations, by copying complex coefficients from the unshifted half-matrix and the realigned shifted half-matrices, as conjugates, into respective second block positions to produce shifted and unshifted full matrices from the half-matrices, including changing a sign of imaginary parts of the copied complex coefficients; aligning and summing overlapping complex coefficients of the unshifted full matrix and the shifted full matrices to produce an expanded frequency coverage matrix; and inversely transforming the expanded frequency coverage matrix from the Fourier domain to produce an enhanced resolution image in the spatial domain. transforming at least three images of the target (1811, 1813, 1815), captured by a sensor in a spatial domain, from at least three phase displacements of the structured illumination along one angle, into a Fourier domain to produce at least three frequency domain matrices, wherein each matrix of the at least three frequency domain matrices comprises a first block of complex coefficients and a redundant, second block of complex coefficients, wherein each complex coefficient of the second block of complex coefficients is a complex conjugate of a respective complex coefficient of the first block of complex coefficients; using estimated reconstruction parameters, applying an inverse mixing matrix to the first blocks to produce at least three phase-separated half-matrices in the Fourier domain, which are an unshifted half-matrix and shifted half-matrices; performing one or more intermediate transformations on the phase-separated half-matrices, including: subpixel shifting, by transforming from the Fourier domain into the spatial domain the shifted half-matrices, applying a multiplication to data in the spatial domain to generate translated data, and transforming the translated data from the spatial domain data back into the Fourier domain to produce realigned shifted half-matrices; and calculating complex coefficients of second blocks in the Fourier domain to produce full matrices from the half-matrices, after the intermediate transformations, by copying complex coefficients from the unshifted half-matrix and the realigned shifted half-matrices, as conjugates, into respective second block positions to produce shifted and unshifted full matrices from the half-matrices, including changing a sign of imaginary parts of the copied complex coefficients; aligning and summing overlapping complex coefficients of the unshifted full matrix and the shifted full matrices to produce an expanded frequency coverage matrix; and inversely transforming the expanded frequency coverage matrix from the Fourier domain to produce an enhanced resolution image in the spatial domain.