#### Problem 1:

Investigating  Aberrations:

Produce a collimated beam of light by expanding the laser beam with the Galilean beam expander.  Position the 1 mm aperture and the f = 38.1 mm plano-convex lens (KPX079) 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 paraxial focus where a very small light spot is obtained and place a target assembly holding an index card at the paraxial focus.  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.  Note the relative positions of the circle of least confusion and the paraxial focus.  Construct a table as shown below.

 aperture in path no aperture no aperture screen at paraxial focus screen at paraxial focus screen at circle of least confusion screen position (mm) diameter of spot (mm)

Repeat the experiment with the lens turned around, so that the convex side faces the aperture.  Comment on your results.

#### Problem 2:

Use the same setup, as in Problem 2.  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.  Remove the aperture and observe how the image changes.  Describe the image.

#### Problem 3:

Modeling With Oslo LT:

Open OSLO LT.  You will be prompted with the following options:

1. Start a new lens – this option will create a new lens defined by the user.
2. Open an existing lens – this option will open a lens by file name.
3. Open the current lens - this option will open the last lens from the previous session.
4. Browse the lens library – the lens library is a list of manufactured lens along with all the optical information about each lens.

Choose option 1. A control screen will appear with three windows.

1. Surface Data
2. Graphics Window (GW 1)
3. Text Window (TW 1)

Highlight the "Surface Data" Window.  All of the options on this window control the surface parameters of the optical system.  The surface data of the lenses used in our experiments can be found on Newport's Web site.

 Diameter (mm) EFL (mm) f/# BFL (mm) FFL (mm) P2 (mm) Tc (mm) R (mm) Model 25.4 38.1 1.5 33.06 38.10 -5.03 7.643 19.690 KPX079 25.4 50.2 1.9 46.03 50.20 -4.16 6.321 25.943 KPX082 25.4 100 3.9 96.97 100.00 -3.02 4.585 51.680 KPX094

You will design a plano-convex lens with a radius of 19.69 mm and thickness of 7.643 mm made of Bk7 glass.

When you start a new lens, the surface window has three rows.  Each row represents one surface:

1. Row 1.  OBJ – This represents the surface parameters of the object, which are set by default for an object an infinite distance from the first optical surface.
2. Row 2.  AST – This is the aperture stop for the system.
3. Row 3.  IMS – This is the image surface.

Your lens system has five surfaces: object, AST, lens with two surfaces, and image surface.  You must add two more surfaces in order to have five surfaces.  Left click the second row, labeled AST, this row will now be highlighted.  Now, right click the same row and a menu will appear.  By choosing the "insert after" option you will insert a surface into the row below the selected (AST) row.  Repeat the process and insert another surface below the surface labeled 2.  Now you have five surfaces:

1. OBJ
2. AST
3. 2
4. 3
5. IMS

Now you can enter surface data.  First, highlight the cell labeled "ent beam radius".  Enter 10 for this value (the default units are mm) by pressing shift and enter simultaneously, or by clicking the green check in the left corner.  The beam radius is the maximum distance between the outer trace rays.  Next, click on the radius for the first lens surface, which is the second column of the row labeled 2.  Enter a value of 0, which will set the radius of curvature for the second surface.  This value can be both positive and negative depending on the surface type.  The next parameter in the current row is the thickness.  The thickness is the distance from the first surface to the second surface.  Enter a 7.643 in this cell, which will put the next surface (surface 3) a distance of 7.643 mm from the first surface.  Next, click the cell in the "glass" column for surface 2 that says air and enter Bk7.

Click on the radius for the second lens surface, which is the second column of the row labeled 3.  Enter a value of –19.69, which will set the radius of curvature for the second surface to 19.69 mm.

Click the "draw off" button and a pop-up window will appear with a drawing of the surfaces.  The aperture stop and image surface are not drawn.  To change this, click the box in the "special" column of each of these surfaces.  A menu will appear.  Choose the "surface control" option, then the "general" option.  Select the "surface appearance in lens drawing" and change the value from "automatic" to "drawn".

In the AST row click the box in the column labeled "aperture radius" and choose "direct specification" and "checked".  "AK" should appear on the box.  Into the thickness column of the AST row enter 10.  This puts the aperture 1 cm in front of the lens.  Into the aperture radius column enter 1.  In the image surface (IMS) row click the button in the thickness column and click auto focus, paraxial focus.  The paraxial focus is at 38.1 mm.  In the aperture radius column of this row change the button to direct specification and then change the radius to 10.

In the graphics window click the "setup window/toolbar" icon and choose "lens drawing".  Then click the "lens drawing conditions" icon (the last icon to the right).  The last three rows have a "rays" column.  Enter 0 rays in the first row and 24 in the third row.  Click some of the draw buttons in the lens-drawing window and examine the drawings.

In the "Surface Data" window go to the AST row.  Open up the aperture stop by increasing the aperture radius up to 10 mm.

Again click one of the draw buttons in the lens-drawing window.  Observe spherical aberration.

In the image surface (IMS) row click the button in the thickness column and click auto focus, minimum RMS spot size.  The distance to the circle of least confusion is 29 mm.  Compare these calculations with your measurements.

In OSLO LT, turn the lens around and again find the distance to the paraxial focus and to the circle of least confusion.  Compare with your data and comment.

Leave the flat side of the lens facing away from the object.  To observe coma, change the field angle in the surface data window to 20 degrees.  In the graphics window choose spot diagram and examine the "graphic spot diagram analysis".  Observe coma in the system.  Comment on your observations and compare with your experimental data.