Related Experiment Video
Updated: Jul 19, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
Published on: January 28, 2019
Reduced-complexity representation of the coherent point-spread function in the presence of aberrations and
Saeed Bagheri1, Daniela Pucci de Farias, George Barbastathis
1Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. bagheri@mit.edu
Abstract:
We introduce a method to analyze the diffraction integral for evaluating the point-spread function. Our method is based on the use of higher-order Airy functions along with Zernike and Taylor expansions. Our approach is applicable when we are considering a finite, arbitrary number of aberrations and arbitrarily large defocus simultaneously. We present an upper bound for the complexity and the convergence rate of this method. We also compare the cost and accuracy of this method with those of traditional ones and show the efficiency of our method through these comparisons. In particular, we rigorously show that this method is constructed in a way that the complexity of the analysis (i.e., the number of terms needed for expressing the light disturbance) does not increase as either defocus or resolution of interest increases. This has applications in several fields such as biological microscopy, lithography, and multidomain optimization in optical systems.
Related Concept Videos
Focusing of Light in the Eye
Geometry of Hyperbolas
Confocal Fluorescence Microscopy
Vector Representation of Complex Numbers
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.
Super-resolution Fluorescence Microscopy
Phase Contrast and Differential Interference Contrast Microscopy
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...

