LensForge™

Tutorial 3 – Analyzing a singlet

BK7 Uncoated Plano-Convex Lens, DIA = 25.4mm, f = 50.0mm

That is really all the information we need to completely specify the lens. We are not yet considering coatings.

Step 1

To start, open the LensForge application by double-clicking on the application icon (if it is in your dock, of course, a single click will do). The LensForge menu bar will take its place at the top of the screen.

For a description of these menu items, see the previous tutorial.

Step 2 - Create a new empty lens file

Next, go to the File menu and select New.

An empty new document will appear. In LensForge, documents have multiple windows. Typically first window you will when you do File > New is Lens data window (unless you have changed the preferences some time in the past).

Step 2 - Give the lens a description

To set the name of the lens you need the System info window, summoned using System > Info. Move the mouse cursor over the text box beside the label "System name" on the System window. Click in the box to make it the keyboard focus (it will acquire a blue outline) and type "Thorlabs LA1131".

Step 3 - Save the lens file

Even before we enter any lens data, we save the file so that it has a name and so that we know we can save it. Go to the File menu and select Save. At this stage, because this is the first time we are saving the file, the Save menu item is actually doing the action of the Save As... item. A sheet will slide down from the title bar of the System window asking you what file name you would like to use, and where you would like the file to be saved. Type "singlet test" for the name, and choose a location (the Desktop, say). Leave the file format as "ZEMAX lens file".

Press the blue Save button to finish the job.

Step 4 - Entering lens data

A lens system consisting of a singlet is analyzed with four surfaces that will be numbered 0 through 3. These surfaces are:

We will analyze the lens for the case of an object at infinite distance.

Make four surfaces

In the Lens data window, press the insert button four times to make four surfaces. After doing that the Lens data window should look like this:

You will note that the Lens data window is divided into an upper and a lower area, separated by a row of buttons (Prev, Next, Insert, etc.). In the upper area is a table and in the lower area are boxes to enter the information that appears in the table, as well as additional information. The lower area has other functions, too. We can ignore the lower area for now.

The column labelled "number" is the number of the surface, 0 through 3. The column labelled "type" is the type of surface. The "STANDARD" type is what we will be using, because it can represent a sphere, so just leave the settings as they are for this tutorial. Other columns give the radius of curvature, thickness, glass, and semidiameter. No "semidiameter" has nothing to do with "radius of curvature": it is how far off axis a ray can be and still pass through the lens. So far everything is zero, even the radius of curvature. Don't worry, zero radius of curvature will be interpreted as planar.

Assign a stop surface

The first thing to do is to assign a stop surface. In lens design this is defined as the limiting aperture of the system and it determines where the rays are aimed. That is why it is critical to put it where you mean to. We will set surface 1 to be the stop. Just click on the row of the table for surface 1. Don't click on any obvious controls, but otherwise it is safe to click anywhere in the row. The row will change color to indicate that surface 1 is selected and the button labelled "Set surface as stop" will become active. Press it. The column labelled "stop" will indicate that surface 1 has become the stop.

Setting surface thicknesses

In LensForge, the "thickness" of a surface is the distance from that surface to the next surface.

Enter infinte thickness for the surface 0 by double-clicking in the column labelled "thickness" in the first row. Type "i" and press return. The word "infinity" will appear, and the table will move you on to editing the thickness of surface 1. Semidiameters begin to change at this point, just ignore them for now.

Enter the thickness 5.3 for surface 1 and press return. Note that you don't type "mm" or anything. All lengths in the table are in mm.

Now, we don't know the thickness for surface 2, so lets put in 10.

Surface 3 is the image, leave its thickness equal to zero. Use the mouse to click somewhere in the table to close the editing. After doing that the Lens data window should look like this:

The thickness of the last surface is not used by LensForge, so just leave it.

Step 5 - Save the lens file

We won't harp on this any more, but it is a good idea to save the file from time to time, as you work on it. Someone might trip over your extension cord.

Go to the File menu and select Save. The file will be saved under its current name.

Step 6 -Set the glass

Double-click in the "glass" column in the row for surface 1. When we type the name of the glass and press enter (or return) LensForge will look up the glass and associate it with the surface. This looking up is case-insensitive, so you can just type lower-case "bk7" and press return. It turns red. That means it did not work: LensForge does not know about a glass called BK7. This is what the Lens data window now looks like if we select the row for surface 1:

The glass name is red and in the lower part of the window, in the little box next to the glass, you see the description "Unknown glass". This failure is not because LensForge is uneducated, it is because the glass vendors do not have a glass named BK7 these days. But there are environmentally friendly glasses with nearly the same name that has replaced BK7. All we have to do is look them up in the catalog.

Looking up a glass

To view the glass library, go to the Tools menu and select Glass library. The glass library will appear:

The table lists every glass in the built-in library, for each glass giving the glass name (also known as glass type), the glass code, and the version, which identifies the vendor catalog from whence the glass came. Already on the first page we can see K-BK7 from Sumita, but let's dig deeper.

The search box at the top of the window will let you restrict the table to those glasses whose name matches the string you type. Type bk7 into the search box. You should see the following:

We see there are two likely candidates for modern-day BK7. Let's pick the Schott one. It is called N-BK7, so we can just go back to the Lens data window and type n-bk7 for the glass for surface 1. Or, as intimated in the upper right hand corner of the glass library window, we can drag the glass from the library and drop it onto surface 1 in the table in Lens data window. It is difficult to communicate a dynamic process like drag and drop in a still picture, but the image below shows where you press the mouse button (the red dot), where you move to (the red line), and where you release the mouse button to drop the glass (the end of the red arrow, over surface 1):

I hope it worked for you. If you had an accident and dropped the glass on the wrong surface, just select Undo from the Edit menu.

Step 6 - Save the file again!

Enough said.

Step 7 - Make a picture

It is time we had a look at the lens we are analyzing. Go to the Analysis menu, Layout submenu, and select Planar. This creates a window showing a planar view (a cross section or projection). By default the section is the YZ plane.

Note that if the glass library window is the front one then the menu item we want will be disabled. This is because the glass library belongs to the application as a whole and not to the lens design document. You will first have to select a window of the document (e.g., the Lens data window) to enable the Analysis menu items.

This is what the planar layout will look like:

You will note that the little numbers just above the picture will change as you move the mouse about. These are the y and z coordinates of the cursor. Also, when you pass over the plane of a surface, the window will show which surface it is just above the image.

The image is not very pretty just yet, we should set the diameter of the lens. Right now it is drawn using the automatically calculated semidiameters. Go back to the Lens data window and enter 12.7 (half of 25.4) for the semidiameter of surface 1 and 2. Now go back to the planar view by clicking on its title bar or selecting the window from the select Windows menu. You can zoom to see the entire lens by selecting Zoom to fit from the Graphics menu or by clicking twice on the Zoom button. Now we have:

Well, it does not look much like a lens and the reason is that we've not yet made the front surface curved. Go back to the Lens data window and enter 25.8 (the prescription curvature) for the radius of curvature of surface 1. Now we have:

Now is looking quite like a lens, but we would like to fill the lens with rays. To do that we must adjust the pupil of the system.

Step 7 - Setting the pupil

Open the pupil control dialog by choosing Pupil control from the System menu. Right now we see that the pupil is being determined by the diameter of the entrance pupil, or rather, the extent of the incoming rays has the specified diameter. This diameter is only 1mm, which is why the bundle of rays on the layout view is so narrow.

The lens is 25.4mm in diameter, but we would almost never use the full lens in practice. Let's use 90% of the diameter, and take 22.8mm as the diameter of the pupil. Change the value to 22.8 and press enter or tab so that the value it taken. Then you can close the pupil control window.

Now the planar view looks like this:

Step 8 - Using a solve

In the above picture it is clear that the last surface is too close to the lens. The rays are converging, but still have a long way to go to focus. To adjust the distance between the lens and the last surface in order to be at focus, we will use what is known as a "solve". In the Lens data table, the column just to the right of the thickness column contains pop-up menus. Each pop-up menu lets you choose what solve to use for the thickness of that surface. Right now they are blank, which means no solve is used.

Click on the thickness solve pop-up menu for surface 2 and release the mouse over "M" to select the "marginal ray height zero" solve. The thickness of surface 2 will automatically update to bring the image plane to the plane of paraxial focus. In the Lens data table you should see

The planar view will look like this after you zoom to fit (double-click on the Zoom button will do it):

You will note that the beam is a bit narrower before the image plane. This is because of spherical aberration: the lens surface is a sphere and so it can not focus perfectly. The focus is blurry (the rays do not focus to a point) and the smallest spot size, or "circle of least confusion", occurs before the plane of paraxial focus.

Step 9 - Making a ray fan diagram

Go to the Analysis menu, Fans submenu, and select Ray. This creates a window showing the result of a transverse ray fan calculation. It should look like this:

The horizontal axis is the pupil coordinate: -1 for the bottom of the pupil to +1 for the top of the pupil, as viewed from the object space. For each pupil coordinate a ray is traced. The y coordinate of the ray when it hits the image plane is plotted against the vertical axis. The meaning of the shape you see is that rays through the top of the pupil hit the image plane too low, and rays through the bottom of the pupil hit the image plane too high. This is the signature of undercorrected spherical aberration. The slope of the curve is zero at the center, which means that the system is at focus for paraxial rays (thanks to the marginal ray solve we put on the thickness of surface 2).

Step 9 - Using the correct wavelength

Up to this point we have been tracing rays assuming that the wavelength of the light is 0.55 microns (the default value). The Thorlabs singlet has a design wavelength of 633 nm, or 0.633 microns. To change the ray tracing wavelength, go to the System menu, and select Wave editor. The window that opens should look like this:

Change the value 0.55 to 0.633 so that we are using the design wavelength for the lens. You will note that the marginal ray solve now gives a slightly different value for the thickness of surface 2 because the focal length changes with changes of wavelength due to dispersive nature of the glass.

Step 10 - Checking the focal length

To finish this tutorial, we will check if the focal length of the lens matches the Thorlabs drawing, where it is listed as 50.0mm at 633nm.

Go to the Analysis menu, Listings submenu, and select Pupil data. We will not go over this information in this tutorial. Here we just note that the focal length is pretty much as specified on the Thorlabs drawing. The difference is within the tolerance of the radius of curvature, which the drawing only gives to one 0.1mm precision.

Conclusion

At the end of this tutorial, you should understand how to enter surface data for an infinite conjugate system into LensForge, how to specify the entrance pupil diameter for your lens, how to specify the wavelength for ray tracing, and how to make layout and ray fan plots.

To learn more, play with LensForge, or try one of the more advanced tutorials as they are published.

By the way, there is any easy way to enter the data for a catalog lens into LensForge, if you have the catalog in ZMF format. You can open the ZMF file in LensForge, make a new lens design and drag the lens from the ZMF file to the empty Lens data table.