Laboratory 4

Aberrations

Objective:

Students will use lenses to observe more geometrical aberrations and chromatic aberrations.

Equipment:

• Laser Assembly
• Beam Steering Assemblies
• Lens Chuck Assemblies
• Target Assemblies
• Lens Kit
• Incandescent Light Source
• Apertures
• Meter Stick, Ruler
• Index Cards

Open a Microsoft Word document to keep a live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

Procedure:

Part 1:

Spherical Aberration

Watch: YouTube, Spherical Aberration

Produce a collimated beam of light by expanding the laser beam with the Galilean beam expander.  Construct the beam expander as in lab 2.  Expand the beam to a diameter between 1 and 2 cm.  Use a  2 inch convex lens. 

• Position the adjustable aperture, adjusted to radius of ~1 mm, and the f = 50.2 mm plano-convex lens (KPX082) in the beam path as close to each other as possible, with the aperture facing the light source and the plane side of the lens facing the aperture. 
• Find the distance from the last lens surface to the location of the paraxial focus, where a very small light spot is obtained, and place a target assembly holding an index card at the paraxial focus.  Estimate the radius of the beam at the paraxial focus.  Enter those data into table 1.
• Remove the aperture and observe how the light rays begin to miss the paraxial focus, forming a much broader circle.  Translate the screen to find the smallest possible light spot, known as the circle of least confusion. 
• Find the distance from the last lens surface to the location of the circle of least confusion and estimate the radius of the beam at that location.  Enter those data into table 1.
• Repeat the experiment with the lens turned around, so that the convex side faces the aperture.  Enter your data into table 1.
• Comment on your results.

Table 1

Coma

Watch:  YouTube, coma aberration

Use the same setup, as in your last experiment.  Let the convex side of the lens face the aperture, then and rotate the lens approximately 20 - 30 degrees.   You may have to re-center the lens.  Place a target assembly holding an index card at the paraxial focus.  Vary the aperture size and observe how the image changes.  Describe the image.

Part 1 Deliverables: (to be included in the your journal)

• Visuals:  Photos or clear sketches showing the beam spot at paraxial focus vs. the circle of least confusion, and the shape of the coma for different aperture sizes.
• Table:  Spherical aberration table 1
• Analysis:  Comparative Analysis/Comments:  A discussion on how the orientation of the lens (flat versus curved side facing the beam) affects the severity of spherical aberration.
  Coma Description:  A qualitative description of the image shape (the "comet-like" tail) observed when the lens is rotated 20-30 degrees and the aperture size is varied.

Part 2:

Astigmatism

Astigmatism appears when extended off-axis objects are imaged with spherical lenses.  

Place the incandescent light bulb with a diffuser and a crossed arrow target onto the optical rail.  Make sure the lines of the cross are vertical and horizontal.  Position a f = 100 mm plano-convex lens approximately 25 cm from the front of light source (the object).  Let a convex side of the lens face the light source to minimize spherical aberrations.  Find the image of the crossed arrows on a screen and note the position of the screen.  Now rotate the lens by ~45 degrees.  Find the position of the screen when the vertical and when the horizontal line is in focus.  Fill in the table below.  Comment on your results.

Field curvature

When flat objects are imaged with spherical lenses, all transverse points on the image are in focus at the same time on a curved surface instead of a flat plane.   Attach a small piece of transparent ruler to the front of the light source.  Position the f = 38.1 mm or the f = 50.2 mm plano-convex lens so that image magnification is greater than unity.  Let the convex side of the lens face the light source.

Do not tilt the lens.  Concentrate on the millimeter tick marks of the image.  Bring the ones in the center into focus.  Then bring the ones farthest to the side into focus.  Note the positions of the screen in each case.  Comment on your results.

Distortion

Distortion results when image magnification is a function of radial distance.  Look at various images of parallel lines on a piece of millimeter paper with the f = 50.2 mm plano-convex lens.  Hold the lens at various distances from the paper creating both virtual and real images.  Describe the distortions you can observe.

Chromatic aberration

Chromatic aberrations are a consequence of the wavelength-dependent refractive index of the glass of the lens.  Different wavelengths come to a focus at slightly different distances. 

Let the light from the incandescent light source pass through an adjustable aperture (the object) and then pass through a f = 38.1 mm converging lens.  Make the aperture as small as possible.  Image the aperture so that image magnification is approximately unity.  Move the screen back and forth around the focus and observe the colors which appear on the periphery of the image.  How does the focal length vary as a function of wavelength?

Part 2 Deliverables: (to be included in the your journal)

• Visuals:
• Tables: Astigmatism table, Field curvature table
• Analysis: Astigmatism:  A comment on the results explaining why the focus shifts for different line orientations when the lens is tilted.
  Field curvature:  An explanation of why a flat object does not form a flat image.
  Distortion:  Qualitative descriptions of tour observations when viewing millimeter paper at various distances for both real and virtual images.
  Chromatic aberration:  A description of the colors seen on the periphery of the image.

Summary reflection:  A final, cohesive reflection at the end of the report summarizing what was learned about the limitations of real-world spherical lenses compared to the "ideal" paraxial model.