Foundational Knowledge

Fundamental Aspects of Airy Disk Patterns

22 May 2024 · 10 min read
  • Widefield Light Microscopy
  • Foundational Knowledge

Abstract

This foundational knowledge article explains the basics of Airy disk patterns in microscopy. It covers how these patterns are generated from an infinitely small focused object point and, how they change with the numerical aperture and wavelength of the illumination. The article also simulates the approach of two Airy disk patterns and explains how to determine the resolving power of an objective lens. 

Key Learnings:

  • The size of the Airy disk pattern changes with the numerical aperture and wavelength of the illumination
  • The resolving power of an objective lens can be determined by examining the size of the Airy disk pattern
  • The Rayleigh criterion is the minimum distance between Airy disk patterns that can be resolved separately

Understanding the Symmetric Airy Disk Pattern and How it Changes in Size

The three-dimensional intensity distribution pattern originating from an infinitely small (sub-resolution) focused object point is symmetrically periodic along the optical z-axis of the microscope as well as radially around it. When this diffraction pattern is sectioned in the focal plane, it is observed as the classical two-dimensional intensity distribution known as the Airy disk pattern. This tutorial explores how the size of the Airy disk pattern changes with the numerical aperture (NA) of the objective and the wavelength of the illumination. It also simulates the close approach of two Airy disk patterns.

Tutorial Guide

In the central image, the tutorial shows two adjacent Airy disk patterns and their corresponding radial intensity distributions (= point spread functions, psf). The patterns, which are close to each other, are generated by green light (546 nanometer wavelength). Below the Airy disk patterns is a simulation of the illumination light condenser light cone and the microscope objective’s front lens. A set of sliders is used to control the tutorial. The Wavelength slider changes the illumination wavelength through a range of 400 nanometers (purple-blue visible light) up to 700 nanometers (red light). At the bottom is the Numerical Aperture slider, which is used to modulate the numerical aperture of the microscope objective.

The Separation Distance slider is used to translate the Airy disk patterns and radial intensity distributions (psf´s) back and forth in the image plane. As this slider is moved to the right or left, the distance between the two adjacent Airy disk patterns either increases or decreases, and the current separation distance in micrometers is shown (both above the slider and in the Airy disk pattern window). Moving the Separation Distance slider to the right causes the Airy disk patterns to move closer together, stopping at the resolution limit. The Airy disk pattern size decreases with illumination wavelength and with numerical aperture. The illumination light cone increases in size as the numerical aperture increases.

Determining Resolving Power with Airy Disk Diffraction Patterns and The Rayleigh Criterion

Each object point is represented by an Airy disk diffraction pattern in the intermediate image plane of the microscope. It follows that the resolving power of an objective lens can be determined by examining the size of the Airy disk pattern formed by that lens. The radius of the Airy disk pattern is determined by the wavelength of illumination and the combined numerical apertures of both the objective and condenser.

In practice, when the specimen is illuminated by a large condenser aperture or behaves as a self-luminous object (e.g., fluorescence sub-resolution beads), the light rays will form adjacent Airy disk patterns. This makes it possible to determine the minimum separation distance that can be resolved with a particular objective by examining the total intensity distribution of closely spaced, or overlapping, Airy disk patterns in the intermediate image plane.

The peak-to-peak distance (Separation Distance, D) between adjacent psf-intensity distribution curves is equal to that between the corresponding Airy disk diffraction patterns. If the radius of the Airy disk pattern is defined as the distance r, and if D is greater than r, then the sum of the intensities of the pair of Airy disk patterns clearly shows two peaks. In the case where the separation distance (D) is equal to the Airy disk pattern radius (r), two overlapping peaks are observed. This condition is known as the Rayleigh criterion, which is the minimum distance between Airy disk patterns that can be resolved separately. If the separation distance is less than the radius of the Airy disk pattern (not illustrated in the tutorial), the intensity distributions merge into a single peak and they are said to be unresolved.


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