Airy Disk

Overview:

Light incident on a circular aperture produces a diffraction pattern described by (ignoring an overall scale factor):

where J₁ is a Bessel function and alpha is given by:

where y is the position on the screen measured with respect to the central maximum, L is the distance from the aperture to the screen, and a is the aperture radius.

Goal of this Experiment: The goal of this experiment is to measure the position of the bright and dark annuli of the diffraction pattern produced by a circular aperture. A schematic of the set-up is shown below.

The PASCO system has a slide (9165D) with two circular apertures with diameters of 0.04mm and 0.08mm.

Suggested Procedures:

1. Set up the apparatus (using the 0.04mm diameter aperture) so that the diffraction pattern appears in the center of the screen.
2. Using a digital camera, take a picture of the diffraction pattern, making sure the scale is visible in the image.
3. Repeat the above using various aperture to screen distances.
4. Repeat the above using the 0.08mm diameter aperture.

Sample Data:

This photograph of a circular diffraction pattern had its brightness and contrast adjusted in NIH Image to make the bright and dark annuli clearer. The diameters of the annuli were measured (in pixels) using the Marquee Tool and the Info Window in NIH Image. A millimeter scale is visible on the right side of the image which was used to determine the corresponding physical size the annuli. In the plot below, the bright and dark regions of the pattern are plotted (appearing as red and gray rectangles). A Bessel function, described by:

which was constrained to match only the center of the first dark ring, is plotted as well.

The Bessel function was also superposed on the photo - keeping the scale true:

Questions:

1. Would the use of a beam spreader help?
2. What is the error in your pixel measurements of annuli size?
3. What is the error in the corresponding physical size of the annuli?
4. How well does the given Bessel function describe the intensity of the diffraction pattern?
5. Would the use of the fiber to gather quantitative intensity information be valuable?