The Optical Resolution Model simulates how two point sources of light appear through a circular aperture, such as those used in telescopes or microscopes. By adjusting parameters such as the aperture diameter, wavelength of light, and the distance between the sources, the simulation demonstrates the diffraction patterns that arise due to wave interference. The model calculates the intensity of light at each point on the observation screen, providing a visual representation of the Airy disk pattern, and allows users to explore the Rayleigh criterion for optical resolution.
\n\nThe Rayleigh criterion provides the minimum angular separation (θ) at which two light sources can still be resolved, and is given by the formula:
θ_{\\text{min}} = 1.22 × (\u03bb / a)
where \u03bb (lambda) is the wavelength of the light, and a is the diameter of the aperture. This formula is crucial for understanding the diffraction limit of optical systems. By comparing the actual angular separation of the sources with this criterion, users can assess whether the sources are resolvable.
The actual angular separation θ between the two sources is calculated based on their distances from the center of the aperture and the distance to the observation screen. First, we calculate the distances r1 and r2 of the two sources from the center of the aperture:
r1 = \u221a((x - xd)\u00b2 + y\u00b2) and r2 = \u221a((x + xd)\u00b2 + y\u00b2)
where xd or d in the slider is the horizontal distance between the two sources, and x and y are the coordinates of the observation point on the screen. r1 and r2 represent the distances from the aperture's center to the two light sources at the observation screen.
The angles for each source are then calculated as:
\n\nθ1 = r1 / L and θ2 = r2 / L
where L is the distance from the aperture to the observation screen. The total angular separation θ is the absolute difference between these two angles:
θ = |θ1 - θ2|
By comparing this angular separation θ to the Rayleigh criterion's minimum value θ_{\\text{min}}, the simulation determines whether the two sources are resolvable. If θ ≥ θ_{\\text{min}}, the two sources are resolvable, otherwise, they are not.
Users can modify variables like the wavelength (\u03bb), aperture diameter (a), and source separation (xd) to see how diffraction limits impact the clarity and separation of the two light sources. The interactive nature of the model makes it an effective tool for studying optical phenomena such as interference and diffraction.
The simulation was originally developed in Java and later converted to JavaScript to improve accessibility on modern platforms. In addition, the new scalar field element introduced in EJS 6.1 allows for a more accurate representation of the intensity fields, enhancing the simulation's educational value.
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