wavefront-reconstruction-from-intensity

Wavefront reconstruction from a single conventional intensity image is generally not possible for an arbitrary optical wavefront without additional constraints, priors, or known optical encoding Verified Answer #1. A standard imaging sensor measures intensity, defined as $I(x,y)=|U(x,y)|^2$, while the wavefront information is contained in the phase $\phi(x,y)$ of the complex field $U(x,y)=A(x,y)e^{i\phi(x,y)}$ Verified Answer #1. Because the intensity measurement discards phase information, multiple different wavefronts can result in the same recorded image Verified Answer #1. This loss of information makes the inverse problem of single-image wavefront recovery underdetermined Verified Answer #1.

Conditions for Single-Frame Reconstruction

Wavefront recovery from a single recorded frame is possible under specific circumstances Verified Answer #1.

• Reconstruction can occur if the object or beam shape is well known and only the wavefront remains unknown Verified Answer #1.
• Recovery is possible if the pupil or aperture is known and the phase is represented using a low-dimensional basis, such as Zernike polynomials Verified Answer #1.
• Phase can be resolved if the optical system encodes phase into intensity in a known manner, such as through curvature sensing, coded phase masks, asymmetric pupils, holography, or microlens arrays Verified Answer #1.
• Reconstruction may be achieved using strong priors or a trained inverse model, though the solution becomes model-dependent rather than physically guaranteed Verified Answer #1.

Physical Limitations

Directly reconstructing the phase at the sensor plane from an intensity image taken at that same plane is impossible because the phase is entirely absent from the measurement Verified Answer #1. Even when the measured image is related to an upstream field through propagation, the inverse problem remains non-unique without constraints Verified Answer #1.