ZEMAX RAY-TRACING EXECRISE NOTES FROM OPTICAL CONSTRUCTION COURSE

RT0

Standard Spot Diagram

Clicking in the ”Standard Spot Diagram” icon under the “Rays & Spot” icon in the Image Quality group under the “Analyze” tab.

You will in this spot diagram see the position of a number of rays originating from the object at the position of the image plane. Information about the size of the spot is given, both in terms of an RMS radius and a GEO radius in the lower part of the plot. The GEO radius is the radius of a circle in the image plane in which all rays fall. The RMS radius is the root-mean-square value of the radius of the positions the rays intercept in the image plane. The latter one is the most relevant. However, it can be worth to note that since a ray tracing program only calculates the fate of certain rays, the values of these two indicators (the RMS and the GEO radii) depend on how many rays the program considers and in which “pattern” they are sent out. There is a standard set of ray patterns and number of rays that the program uses, but one can also chose other sets. You can toggle between three such patterns in the Setting window, which you open by clicking on the small downwards arrow in the upper left corner of the window of the Spot Diagram. Alter between, “Squared”, “Hexapolar”, and “Dithered”, and see the effect of this. You can also increase the number of rays. For a simple system like this, the extra time it takes to calculate more rays than the predetermined value of 6 is negligible. Therefore, use to some larger value, e.g. 24, and see the effect. Use “Dithered” and a ray density of 24. What is the RMS size of this spot (you should get an RMS spot size between 200 and 400 µm, if not, redo)

“Solve” routine

There is also another way of finding the paraxial position of the image (instead of using the optimization routine), namely to use a “Solve” routine. To use the “Solve” routine, double-click on the small square box of the cell you just optimized (the thickness cell of row 2) and, instead of using “Variable”, chose “Marginal Ray Height”. This solve-routine will help the program to find the value of the lens-to-image distance that forces the marginal ray (the marginal ray is the ray that originates from the optical axis and passes the aperture stop/entrance pupil at a given height/pupil zone, in general at the rim of the aperture stop/entrance pupil) to arrive at a height given by the “Height” value in the image plane. We want to find the paraxial focus. Hence, the ray height should be specified to 0 (which is the default value).

Next to specify is which ray should be considered. You specify this by specifying a “Pupil Zone” value. We know now that the paraxial focus is the position for which rays with a virtually zero angle focus to one spot (all higher order terms become negligible). The “Pupil Zone” value refers to the (normalized) height of the beam in the entrance aperture (the STOP surface) of the system. We get rays with 0 angles, and hence the position of the paraxial focus, by specifying the Pupil Zone” value to 0. Therefore, run “Marginal Ray Height” with zeros for both the “Height” and the “Pupil Zone” values.

RAY- RACING USING ARAXIAL SURFACES

The ZEMAX program has also a possibility to use non-spherical surfaces (as for example, adding a small conical behavior to the spherical shape that will compensate for many types of aberrations).
But, it has also the sometimes useful feature of introducing completely aberration-free surfaces (i.e. a surface that exactly follows theparaxial theory). These are called paraxial surfaces.

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RT1

Create a Lens Data editor that describes the situation. Start by making a lens made out of
two lens surfaces, each of them of paraxial type (and each having half the refractive power, i.e., twice the actual focal length, i.e. 40 mm), but, with no distance in between. This is
convenient when comparisons with finite thickness lenses are going to be done later on. Select an “Entrance Aperture Diameter” of 10 mm under the “Aperture“ tab of the SYSTEM
EXPLORER. Place the image plane at a so far arbitrary position behind the lens, e.g. at 100 mm. For display purposes, you can make the lens larger than the minimum size. Give the lens, for simplicity, a semi-diameter of 8 mm.

run the optimization procedure (do not forget to start with the “Optimization Wizard” icon in the Automatic Optimization group under the “Optimize” tab, and use Type: “RMS”, Criteria “Spot Radius”, and Reference “Chief Ray” as be-fore, and use 4 rings, before you run “Optimize!” in the Automatic Optimization group under the “Optimize” tab) and find out where the image plane is localized. Look also at the Layout.

Determine the transverse magnification

In order to determine the transverse magnification of the system, you need to place another object at a certain distance from the optical axis. Open the “Fields” tab in the SYSTEM EXPLORER. The type of field chosen under “Settings”should be “Object Height”. If not set, change to this. By default, you have one field point set (termed Field 1). If you open this tab, you will see that this field point is at x = 0, and y = 0, and that it has a weight of 1. Now you need to create another field point. Open the “Add Field” tab and set this at x = 0, and y = 10, with a weight of 1. Note that you have to click on the Enable box, be able to set this field point.

Remember this for the future. Every time you alter the number of field points (or the number of wavelengths, see coming exercises) you need to open and run the Merit Function Editor again.

the actual position of the rays from the uppermost part of the object can, for ex-ample, be found by invoking the ”Standard Spot Diagram” icon under the “Rays & Spot” icon in the Image Quality group under the “Analyze” tab. You should be able to read the center position of the beams both at the object and the image plane. The ratio should give you the transverse magnification. Which transverse magnification does this system have?

Fixed L = SIM + SOB

In this case you need to optimize an intermediate position (i.e. that of the lens) while holding the object-to-image distance fixed. You can accomplish this by double clicking on the Thicknesscell of the last lens surface and choose “Position” instead of “Fixed” or “Variable” that we have used before. You can here determine the position from another given surface. Choose “From Surface:” “0” and “Length:” “160”. This implies that the image plane always will be positioned 160 mm behind the object plane. Hence, you can now optimize the position of the lens as you want. Change the Thickness cell of the uppermost row to “Variable” so that you can optimize the position of the lens. A possible starting point (if you model your lens as two surfaces) could then look like as foll.

Add the magnification constraint

One way of doing this is to open the merit function(in Wizards and operand)and then add one more opti-mization condition (the magnification constraint). This you can do by adding one more line in the merit function. This line should be the first line. Click in any of the cells in the DFMS line. Press “Insert”. They you get a dummy line, with the command BLNK (for Blank) as the type. You need to exchange this to some more useful command. Click in the small squared box of this cell. You should then get a list of possible optimization operands. These you can use at any time in your ray tracing (you can read about this in the help files). In this case, use PMAG, since this puts a requirement on the paraxial magnification. This magnification we want to lock to -0.5. Therefore, type PMAG for the “type” of this operand (in place of BLNK). You need to give the target value of this, which thus is -0.5. Type this in the target column. Then you need to give it a weight. Give it a weight of 1 (which is a standard value). Now when you run the optimization, the program will both try to minimize the spot size in the image plane (or the aberrations) but also try to accomplish a system with a paraxial magnification of -0.5. Run the optimization and determine the focal length and the lens position.

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RT2

Remember that in order to get the focal length of such a system (which is a parax-ial quantity), you have to look at rays that go close to the optical axis. This you can do either by using the optimization routine for the focal length (with the radii of curvature of the first surface as a variable, with the second surface having the same radius of curvature but with opposite sign, which can be done by the “Pick up” routine, with a fixed value for the distance between the last surface and the image plane, and with a very small entrance pupil diameter) or by using the Solve routine for the marginal ray height (“Marginal Ray Height”, 0,0) and manually trying various radii

Creating a parallel pencil of rays

let the object have an in-finite distance to the first surface, which also is the “Aperture Stop” (also called the “Surface Stop” in ZEMAX). If you want to see some parts of the parallel rays falling in on your lens system (in the Layout window) you can add an extra non-refractive dummy surface in front of the lens. This non-refractive surface, which can serve as the entrance pupil, should not refract the rays. Hence, it should be fol-lowed by only air (no glass material). It should, however, have a certain distance to the lens. This distance can be quite arbitrary (since parallel light rays are emerg-ing from the surface) so as to create a nice layout.

Insert therefore a new surface directly after the object surface. (Click in any cell of surface 1 and press the “Insert” key on the keyboard.) Type a suitable number for its thickness in the“Thickness”column. Any number in the range 10 to 50 will suffice. Make sure that the distance from the object to the first “dummy” surface is infinite. Let this time the dummy surface be the ”Aperture Stop”. You do this by double clicking in the first cell of the row, which reads “1”, (or by marking any cell of row 1 and then opening the “Settings” window, which you do by pressing the arrow that points down enclosed in a circle (i.e. ) and click in the box for the “Make Surface Stop”. You will find that the surface stop has changed from the first surface of the lens to this new fictitious surface. When you look in the Layout window, make sure you plot the optical system from surface 1 to surface 4 (see the “Settings” window). We will come back to the importance of the” Aperture Stop”in later Ray Tracing exercises.

One why to find this is to use the optimization routine you used in a previous Ray Tracing exer-cise, another is “Marginal Ray Height” solve (for the latter, double-click on the small square box of the thickness cell of the last surface of the lens and choose “Marginal Ray Height”)

Set Surface Stop

Make sure that the lens is the “Surface Stop”. (If not, double-click in the first cell of the first surface of the lens, i.e. the cell that reads “Paraxial”,and then click in the “Make Surface Stop” box.

Optimize the system

When you optimize the system, do not forget to start with the “Optimization Wiz-ard” icon in the Automatic Optimization group under the “Optimize” tab, and use Type: “RMS”, Criteria “Spot Radius”, and Reference “Chief Ray” as before, and use 4 rings, before you run “Optimize!” in the Automatic Optimization group under the “Optimize” tab

Report

You can find information about the positions of the principal planes of an optical system in “Prescription data”, which you find under the under the “Re-port” icon in the Reports group under the “Analyze” tab. and thereby check that the equation you derived above is correct.

Example

Open the “Cooke 40 degree field” lens (one of the example files that are supplied with the program, can be found under Zemax\sample\sequential\objectives)1 and look at the layout window. This system shows the basic design of a real Cooke .triplet. One positive lens, one negative lens (made of another glass material so as to minimize chromatic aberrations, something you will look closer to in a comingray tracing exercise) followed by one positive lens finally. You can see how light from three different angels (from far away, e.g. infinity) propagate through the system. Please hold this system in your mind when you are working with the sim-plified paraxial lenses in the exercise below (so you do not lose grip of the reality).

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RT4

Specify that the wavelength of the light

Specify that the wavelength of the light is 587.562 nm. This you do by opening the “Wavelength”tab in the SYSTEM EXPLORERand then, under “Settings” and“Preset”, select “d(0.587)”. When you have selected this as your primary wave-length, press the button “Select Preset” to execute this choice. You can see that you have selected this wavelength as your primary wavelength if the text in the next tab “Wavelength 1 (0,xxx μm, Weight = 1,000)” displays this wavelength, i.e. if it reads “Wavelength 1 (0,588 μm, Weight = 1,000)”.

Material catalogue

The reason for this particular wavelength to be of special importance is that it cor-responds to a yellow line in the spectrum from helium (at 587.5618 nm). The in-dex of refraction at this wavelength is commonly abbreviated dn. Find out what the actual index of refraction of BK7 is at this wavelength, i.e. determine the dn - value. (There is an extensive catalogue with many types of glasses, termed “mate-rial catalogue”, incorporated into the program that can give you a lot of useful in-formation. Remember that BK7 is a Schott glass.)

Find a particular glass

he easiest way to find a particular glass in this catalogue is to type BK7 in the Material column in the Lens Data editor and then mark the name of the glass be-fore you open the material catalogue. It then opens directly with information about this particular type of glass at this particular wavelength, i.e. with info about n_d. alternatively, if you type BK7 in the Material column in theLens Data editor, you can also find its index of refraction for the wavelength used (thus not only at 587.5618 nm) in “Prescription data”, which you find under the under the “Re-ports” icon in the Reports group under the “Analyze” tab. Look about half down the document. Check that you can find the value of the index of refraction at both places.

The (RMS) spot size of the focus

The (RMS) spot size of this focus (look in the ”Standard Spot Diagram”icon under the “Rays & Spot” icon in the Image Quality group under the “Ana-lyze” tab and use “Dithered” as “Pattern” under “Settings” and a ray density of 24)?

Selecting “F, d, C (visible)”

Expand now the number of wavelengths you are using to 3. In the “Wavelength” tab in the SYSTEM EXPLORER you should use 486.1 nm as wavelength number 1, 587.6 nm as wavelength number 2 and 656.3 nm as wavelength number 3 (the yel-low helium line and the blue and red hydrogen Fraunhofer lines). Make the 0.5876 μm wavelength the “primary” one. Note that you can get all these three wave-lengths directly by selecting “F, d, C (visible)” under “Settings” and “Preset”. When you have pressed“Select Preset” you should get three lines(tabs) of wave-lengths below the “Settings” tab reading“Wavelength 1 (0,486 μm, Weight = 1,000)”,
“Wavelength 2 (0,588 μm, Weight = 1,000)”,
“Wavelength 3 (0,656 μm, Weight = 1,000)”

Select all wavelength

there is a “Wavelength” box in the upper right most corner in which you can specify which wavelengths you want to study. Choose “All”. You need also to choose “Wave #” in the “Color Rays By:”box. Do the same with the “Spot Diagram” window (and use again “Dithered”and a “Ray Density” of 24). You are now ready to see what happens with all the light beams in the system.

Update all widows

(double click in them or use the fast red button with two curly arrows in theQUICK ACCESS TOOLBAR).

Dealing with chromatic aberration.

There are two different windows that are of particular use when dealing with chromatic aberration. The first one is called “Focal Shift” and can be opened by invoking the ”Chro-matic Focal Shift” icon under the “Aberrations” icon in the Image Quality group under the “Analyze” tab. This window shows you the shift in focal length as a function of wavelength.
The other useful window is the “Through Focus Spot Diagram” and can be opened by invoking the” Through Focus Spot Diagram” icon under the “Rays & Spot” icon in the Image Quality group under the “Analyze” tab. This window shows you five different spot diagrams. Adjusting some parameters under “Set-tings” (the arrow that points down enclosed in a circle, i.e. the ) will give you a nice result. Choose a ”Ray Density” around 5 - 10 (depending on your monitor), ”Delta Focus” to 500 (μm), do not select “Use Symbols”, use “Pattern:” “Dith-ered”, and make sure that “Wavelength” is set to ”All”. Depending on your moni-tor, you can play around with the line thickness, it is often easiest to see this if you select the “thin” or “thinnest” line thickness (change “standard” to “thin” or “thin-nest”).
What you will see is how the spot diagrams look like in focus, as well as 500 and 1000 μm in front of and behind the focus. As you see in this case, the focus of the green wavelength (i.e. the one at 587 nm, the middle one in wavelength) is close to the selected image plane (i.e. in focus), the blue wavelength (486 nm) has a fo-cus about 1 mm in front of this focus while the red one (656 nm) has its focus about half a millimeter behind the selected focus. This is a pictorial illustration of what the “Through Focus Spot Diagram” shows.

Effective focal length by using marginal ray angle

Select now somewhat more suitable thicknesses of the lenses: 3 mm for the first one and 2 mm for the second one. The actual focal length will then change. Reop-timize the optical system so that you get a focal length of exactly 100 mm by let-ting both the first radius and the distance between the last lens and the image plane be variable, make the first lens symmetrical, i.e. 11RR′= − (by a pick up of the first surface), let the lenses be cemented, i.e. 21RR′=, and use a “Marginal Ray Angle” solve of the radius of the last lens surface of -0.1. The “Marginal Ray Angle” solve is a useful way of getting a certain effective focal length. A “Mar-ginal Ray Angle” solve of the radius of the last lens surface of -0.1 should give you an effective focal length of 100 mm. Spend some time thinking about whythis is the case. What does a marginal ray angle of -0.1 imply?

RT5

Standard Spot Diagram

The GEO radius, given in the lower part of the plot, gives the radius within which all the rays are collected. Hence, the GEO radius gives information about the dis-tance to the ray that is farthest from the central reference point. This radius thus corresponds to the maximum ray aberrations Yε and Xε defined in the course material.The RMS radius, on the other hand, gives a root-mean-square value of the radius of all the rays. The RMS radius is often a more useful and representative entity since it gives a weighted distribution of the rays.

Through Focus Spot Diagram”

The “Through Focus Spot Diagram” shows you the spot diagram from a number of rays emerging from one (or a selected number of) single point in the object plane not only in the image plane but also at a few planes in close proximity to the image plane. This menu is particularly useful in systems where some rays will fo-cus in front of the chosen image plane while others focus slightly behind, as oc-curs for “Chromatic Aberrations” as well as a few of the monochromatic aberra-tions, e.g. “Spherical Aberration” and “Curvature of Field”.You will address these in detail in future problem sets. When you invoke this window for the single lens, you will find two rows with five spot diagrams in each. Each spot diagram in each row s calculated for a specific position with respect to the chosen image plane. The middle one is exactly at the position of the image plane. The other ones are the spot diagrams as they look in front or behind the image plane. The two rows correspond to the two fields. In the ”Settings” menu there is a box for specifying the shift in position between each of these diagrams (“Delta Focus”) in units of μm. Select 1000 μm and make sure you are looking at the single lens. Select “Dithered” and a suitable “Ray Density” also in the “Options” window (12 is fairly OK). You can switch be-tween to ”Use Symbols” and not to “Use Symbols”, and to use “All” or one wavelength at a time in the “Wavelength” box to see what you think is best for your particular application. Start with the single lens.

Enclosed Energy

The program gives the user also the possibility to investigate the amount (or frac-tion) of rays in a fan that hits the image plane within a certain radius from the spot. This is referred to as “Enclosed (or Encircled) Energy”. Under the Image Quality group under the “Analyze” tab you can find the “Enclosed Energy” icon. Under this, you can find few different types of “Enclosed Energy” diagram of which two are “Diffraction” and “Geometric.

Optical Path

The program can also display cuts through the “Wave Map”, so called “OPD Fans” (“Wave Aberration Sections “in the course material) or “OPD” diagrams, where “OPD” stands for “Optical Path Difference”. This can be opened by invok-ing the “Optical Path” command under the “ “Aberrations” icon in the Image Quality group under the “Analyze” tab. They will give you information about the optical path difference along the tangential and sagittal cuts at the exit pupil (the two orthogonal directions of the “Wavefront Map”). If more than one wavelength is used, one curve for each wavelength will be dis-played. Look at the “OPD Fans” for the two lenses. Look not only at the shapes of the curves for the two optical systems; pay also attention to the maximum scales (which sometimes can be more important than the actual shapes).

Ray Fan

The program can also display cuts through the “Spot Diagram” display. The “Ray Fan” window can be opened by invoking the “Ray Aberration” command either under the “Rays & Spot” icon or the “Aberrations” icon in the Image Quality group under the “Analyze” tab. This window shows plots of the ray aberration (defined as the difference between the actual image point and the image point of the chief ray in the image plane) as a function of the height of the exit pupil.The “Ray Fan” curves are also the derivatives of the OPD curves discussed above. You get three curves in each diagram (corresponding to the three wave-lengths), one diagram for each plane (tangential and sagittal) and one pair of dia-grams for each field (bundle of ray direction). Compare the “OPD” curves with the “Ray Fans” and make sure you understand how they are related.

Field Curvature and Distortion

The “Field Curvature” and “Distortion” aberrations can be display by the com-bined “Field Curvature and Distortion” command. This command can be found under the “Aberrations” icon in the Image Quality group under the “Analyze”tab

RT6

OPD Fans

The program can also display cuts through the “Wave Map”, so called “OPD Fans” (“Wave Aberration Sections “in the course material) or “OPD” diagrams, where “OPD” stands for “Optical Path Difference”. This can be opened by invok-ing the “Optical Path” command under the “ “Aberrations” icon in the Image Quality group under the “Analyze” tab. They will give you information about the optical path difference along the tangential and sagittal cuts at the exit pupil (the two orthogonal directions of the “Wavefront Map”).

RT8

Effective Focal Length)

When you optimize, always use the default sequential merit function with RMS spot radius referenced to the chief ray. To make systems with the same effective focal length, add the operand EFFL (Effective Focal Length) with target 105 on the first line in the merit function editor (make a new line before the DMFS line and type EFFL in its first box). Use a weight of 1 for the EFFL command.

Prescription data

or every lens that you design, make data sheets that include the most relevant in-formation, which should at least consist of •information about the lenses (radii, types of glass, distances, etc), •a layout, •OPDs, •Ray fans, •spot diagrams, and •a short compilation of the Seidel coefficients. One way of documenting the information about the lenses (radii, types of glass, distances, etc., i.e. the lens data editor) is to open the “Prescription data”, which you find under the under the “Report” icon in the Reports group under the “Ana-lyze” tab., since this contains the lens data editor. You can then save this in text format somewhere, and cut the lens data editor from this text file and past it into your text editor. You can do the same to retrieve the Seidel coefficients from the “Seidel coefficient” window, which can be found under the “Aberrations” icon in the Image Quality group under the “Analyze” tab.