Meaning
Optical wavefront profiling relies on dividing an incoming beam into a grid of localized sample points. A Shack-Hartmann matrix represents the mathematical relationship between the measured spot displacements on a sensor array and the reconstructed phase profile of the light. This formulation is used in adaptive optics to calculate real-time correction signals.
Subaperture Gradient
Each lenslet in the sensor array focuses a portion of the wavefront onto a detector. The displacement of each spot from its reference position is proportional to the local gradient of the phase. A Shack-Hartmann matrix relates these individual gradients to the global shape of the optical wavefront.
Wavefront Reconstruction
Reconstructing the phase profile from the measured gradients involves solving a system of linear equations. The inversion of the Shack-Hartmann matrix, often performed using singular value decomposition, yields the phase values across the aperture. This reconstruction must be executed rapidly to enable real-time wavefront correction in astronomical imaging.
The computational efficiency of this matrix inversion directly affects the closed-loop bandwidth of the adaptive optics system.
Modal Coefficient
The reconstructed wavefront is often represented as a linear combination of Zernike polynomials. The columns of the Shack-Hartmann matrix map these polynomial modes to the expected spot displacements on the sensor. This modal representation facilitates the correction of common aberrations like defocus and astigmatism.
