Conventional wavefront correction uses direct wavefront sensing methods such as the Shack-Hartmann sensor to measure the wavefront at the pupil of the system. Image sharpening is an indirect wavefront sensing method where the wavefront correction is performed using measurements from the image plane. Wavefront correction using image sharpening is advantageous in systems where a point source isn't available or where the number of optical components needs to be reduced by using the scientific camera that is already in place. Correction is performed by measuring the sharpness value as the correction device, such as a deformable mirror, cycles through until the sharpness value is maximized and continues to adapt as the aberrations change. A sharpness metric, or definition, is needed to measure the sharpness value such that it reaches a maximum when aberrations are minimized. This work investigates the use of the Fourier transform of the image, the image spatial frequency spectra, as a Fourier-based sharpness metric. The image spatial frequency spectra is obtained two ways, digitally by computing the Fourier transform of the image plane and optically with a coherent source by using the Fourier transform properties of a convex lens. Affects of aberrations on the intensity at various spatial frequencies are investigated to obtain a sharpness metric that reaches a maximum and aberration strengths decrease. Results from experimentation of various optical configurations are presented to evaluate the performance of these Fourier-based metrics.
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