Meaning
Deterministic phase-retrieval methods use a partial differential equation to calculate the phase profile of a coherent or partially coherent wave from measurements of its intensity at multiple propagation distances. This mathematical framework, known as the transport of intensity equation, offers a non-interferometric path to quantitative phase imaging, avoiding the complex setup and vibration sensitivity of traditional interferometers. By measuring the axial gradient of the intensity along the direction of propagation, the phase of the wavefront can be recovered through numerical solver algorithms.
The application of this method is constrained by the requirement that the paraxial approximation holds and that the intensity remains non-zero across the field of view.
Algorithm Execution
Numerical reconstruction solves the transport of intensity equation by utilizing fast Fourier transform techniques to invert the Laplacian operator. This computation takes the difference between intensity images recorded at slightly underfocused and overfocused planes to approximate the axial derivative. The resulting phase map yields a direct representation of the optical thickness or specimen height, enabling the inspection of transparent polymers and biological samples.
Metrology Benefit
Instrument designers build compact phase-contrast microscopes that lack the reference arms of standard interferometric setups, reducing mechanical complexity.
Numerical Constraint
Spatial resolution depends heavily on the accuracy of the axial derivative approximation.
