dbOptic Optical Design Software Tutorial

dbOptic Software Tutorial

Spend a few hours with this tutorial and you will become well-acquainted with most of the features of dbOptic. It is suggested that you print this document so that you can make notes as you go and have easy reference to the tutorial steps. It is recommended that you step through this tutorial before making new or importing additional designs to the dbOptic database.

Syntax for this tutorial is as follows:

Menu Commands are shown within < > symbols. For example, <File><Print> means "go to the File Menu Command and select the 'Print' sub command" shown there. Other controls on the form are identified by the identifying label next to the control, displayed between square brackets. For example, the "Object Medium" Textbox in the tutorial steps would be identified as [Object Medium].

Keyboard commands and data entry are displayed within single quotes. 'ENTER' means that you are to press the "Enter" Key. '1.25' means to key in the value only, without the apostrophe marks. 'Dn' and 'Up' refer to the "Down" and "Up" cursor keys on the keyboard near the 'CTRL' key (not the arrow keys on the numeric keypad).

LESSON #1. The purpose of this lesson is to gain familiarity with features and controls on the primary design screen of the program.

Informational notes:
Upon starting the program, an optical prescription (referred to as an "Rx") is displayed in the Graphics Window. The Rx displayed will always be the Rx that was open at the time the program was last shut down. The Rx displayed is called the "Current Rx". Surface data do not appear on opening, but can be displayed after clicking [+].

dbOptic Main Optical Design Screen

Start dbOptic if the program is not already open. After startup, the design screen with a design prescription in the Graphics window will be displayed. Press the [+/-] key to "expand" the current design and show surface data for that design. Your screen should appear similar to the above figure, but with a different design showing.

Press [Up] or [Dn] to change the Current Rx and note the change in the Graphics Window and and in the Rx Detail Grid each Rx as it is displayed.
Use the mouse cursor to click on the scroll bars on the right hand side of the Rx Grid to display additional designs, then click on various rows within the Rx Grid to make the Rx shown in that row the Current Rx.
Select <File><Find Rx>. In the dialog box which opens, key in 'AO1' to open the Rx with name AO1, then [OK]. The doublet design is displayed. Note: Rx Names are case-independent. That means that there is no difference between 'AO1' and 'ao1'.
Click on the 4 different surface records within the Rx Detail Grid. Note that the current surface is indicated in two places: (1) the [Current Surf] field and (2) when the current surface number is greater than 1, a pair of triangular arrows point to the edge of the current surface in the Graphics Window. Note incidental to this tutorial: When comparing Surface #2 and #3, note that since the distance from Surf#2 to Surf#3 = 0 and the two surfaces are identical, we have a "contact" achromat with no air space between elements. If we wanted to, we could delete Surf#2 without making a material change to the Rx.
Note that the Rx Grid shows the design focal length, diameter of Surf#1, measurement units and the design wavelength for this Rx. Now find the drop down box [Design nm], click on the down arrow and select a different design wavelength. Note that the design focal length value changes in the Rx Grid. This is due to the change in the paraxial image position for the new design wavelength.
Now find the [units] text box located to the left of the [Design nm] field and select the alternate units shown. The surface detail list closes. Open it by clicking on [+] and note that the focal length and diameter shown in the Rx Grid and the surface data are changed from "inches" to "mm".
Note that moving the mouse cursor within the Graphics Window changes the value shown in the [X-Val] and [Y-Val] text boxes on the right side of the form. The values shown are the X and Y distance from the vertex of the current surface to the mouse cursor position. If you select Surface 3 from the Rx Detail Grid and then position the mouse cursor at the vertex of Surface 4, note that [X-Val] = Distance for Surface 4 which is the distance from Surface 3 to Surface 4 (thickness of the second element making up this doublet).
Sorting. Move the mouse cursor over the column headings in the Rx Grid and note the display of the bold down arrow. Click on one of the headings to sort all of the designs in ascending order of the column heading clicked on. Now hold down the 'CTRL' key and do the same. Sorting is now in descending order. Note that if you sort on the Dia(1) or Design FL columns, that the sorts take into account the units of each design, properly listing them in ascending or descending order. Note also that the sort function is also available from the <View> Menu. Finally, sort on the [Rx Name] field to restore normal order of designs in the Rx Grid.

LESSON #2. The purpose of this lesson is to show how to create a new design and enter surface data.

Select <File><New Rx>. Enter 'a new lens' as the Rx Name in the dialog box that appears. A Hint Message Box immediately appears, advising you that after entering surface data for Surface #1, you are to click in the plot area [Graphics Window] to set the position of the vertex of the first surface. Hint messages have been included to help guide you while you are learning the features of dbOptic. After you become an experienced user, you can suppress the display of Hint Messages by making an appropriate change to the program defaults using the <View><Defaults> Menu item. Click [OK] to close the hint message. Note that the Graphics Window is cleared and that a Surface 1 record is added to the Rx Detail Grid with "New" as the Surface Type. This Surface Type must be changed to one of the values 'Sphere', 'Flat', 'Iris', 'Ellipse', 'Parabola', 'Hyperbola' or 'General'. You may make this selection by either (1) typing the first letter of the desired surface type or (2) double-click in the field repeatedly until the desired surface type appears.
Select 'Sphere' by typing an 'S'. The text cursor advances to the [Medium] column. Key-in 'BK7', then click in the [Diameter] column and key-in '40'. We will skip the Distance column for Surface 1 because Distance is always zero for Surface 1 of any design. Click in the [Rc] column (for Radius of Curvature). In the Rc column, you may key-in the actual radius of curvature value or you could instead enter "1/" followed by the curvature value for this surface. We will key-in an actual Rc (key in '80'). Then move the mouse cursor into the Graphics Window, somewhat left of center, and click to place the vertex of Surface #1. Note that Surface #1 is drawn in the Graphics Window and that a new surface is added to the Rx Detail Grid with Surf Type = "New", awaiting data entry for that surface.
For Surface #2, double click in the [Type] column until 'Flat' appears. Use the [Tab] key to tab through to the [Diameter] column. Note that after tabbing past the [Medium] column, you were prompted to enter a medium in that field. Enter 'AIR' in the field. Note that [Diameter] was updated automatically using diameter of the previous surface, but could be changed if needed. Tab through to [Distance] and enter '6'. The [Rc] value for flat surfaces is always zero. Now click anywhere in the Graphics Window to update the Rx drawing.
With the Surface Record Selector showing Surface #3, enter values identical to Surface #1 (except for [Distance]) : Select 'Sphere', 'BK7' , '40', '30' for [Distance] and Rc = '80' and click in the Graphics Window to update the design. Now complete the element by entering 'Sphere', 'AIR', '40' , '6' and '60' for Surface #4 and click once again in the Graphics Window.
Note that we now have a design made up of 2 separated elements, both with diameter = 40 mm. As the last steps in this lesson, select <File><Save> to save the design. Note that the "New" last surface has been deleted and that the <Edit> Menu, which had been disabled before the <Save> event is now enabled. Key-in 'Lesson #2' in the [Reference] field of the Rx Grid for this Rx.

LESSON #3. The purpose of this lesson is to learn about the design editing features available from the <Edit> Menu.

Note: if the background color of the Graphics Window changes from white to black, you may have inadvertently activated the <Trace> Menu. If this occurs, simply select <dbView> from the <View> menu to restore to database view.

In Lesson #2, we learned that it easy to append additional surfaces to any new design. However, if we must insert a new surface in the middle of the design or turn an element over so that, for example, Surfaces #3 and #4 are reversed, we would find that we cannot easily make these changes in the Rx Detail Grid without reentering data in the affected records to reflect the revisions. With 'a new lens' as the Current Rx, first select <File><Save As> to make a copy of the design. Key-in '2 Elements' and click 'OK'. Note that the new Rx Grid record is displayed, identical to the next record in all respects except for the Rx Name. If the [+/-] button is showing as [-], click on it to hide the Rx Detail Grid.
Select <Edit> to redisplay the Rx Detail Grid. Click on the Surf #3 record in the grid, then select <Edit><Flip><Element>. Click 'OK' to confirm your decision and note that the entries in the Rx Detail Grid have been changed and the design redrawn to reflect the requested editing change: The Rx is redrawn with the second element "flipped over". Note that this resulted in a slight change in focal length as well. Now click on Surf #2 in the Rx Detail Grid and select <Edit><Move><Train>. A 'Train' is defined as all of the surfaces from the currently selected surface to the last surface of the Rx. After acknowledging the dialog messages, move the mouse to the right of Surface #2 until the distance from Surface #1 as indicated in the [X-Val] field is slightly greater than 13, then click. Note that the Rx is redrawn again with the first element thicker. We can also change any of the Surface data by making direct changes in the Rx Detail Grid: Click in the [Distance] field for Surf #2 and key-in '14'. Then click anywhere in the Graphics Window to update; then <Save>.
Open the Detail Grid and advance to Surface 2. Select <Edit><Insert or Append><Surface>. A "blank" record for the new Surf #3 is displayed after clicking 'Yes' in the dialog box. Enter [Type] = 'Flat', [Medium] = 'BAK1' , [Diameter] = '35' and [Distance] = '15'. Click in the Graphics Window to update We could insert another surface after the last with medium 'AIR' and end up with 3 separate elements. Instead, select <Edit><Undo> which will revert to the last saved version of the design.
We will now add a library (database) design to the Current Rx in the space between Surface #2 and Surface #3: Click on the Surf #2 record in the Rx Detail Grid. Select <Edit><Insert or Append><Library Item>. In the message box that is displayed, note that you will select the item to insert by clicking on it in the Rx Grid. You may sort the records in the Rx Grid or use the scroll bars to help find the Rx to insert, but if you click within the grid, the program will want to insert the first Rx that you clicked on. Find "Cooke Triplet" under the list of Rx Names and click on it. A message box will ask to confirm your decision. Click 'OK' and note that three new elements now appears after Surf #2, with the first in contact with Surf #2. Click to move the new element about 3 mm (use X-Val) from Surf #2. Note that although the units in the Current Rx are "mm" and we inserted a non-metric design (in), the program performed the necessary conversions during the insertion procedure.
Now let us delete the first two surfaces by selecting <Edit><Delete><Element> after first making sure that Surf#1 is the current surface. Then select <Edit><Flip><Rx> to turn the design completely around so that Surf #1 becomes Surf #8, etc. Then select <File><Save> to save the changes. Our design now contains four elements, so select <File><Save As> and copy the design to the new name '4 Elements'. Then find the '2 Elements' design in the Rx Grid and make it the current Rx. Then hold down the CTRL key and press the letter 'D' key to delete the '2 Elements' design (Same as selecting <File><Delete Rx>.
For the next step in this lesson, we will locate the '4 elements' design and make a focal length change. First make '4 elements' the Current Rx. Then select <Edit><Rescale><Focal Length>. The current focal length is displayed in the dialog box which opens. Key-in '400' to replace the current value shown and click 'OK'. Note that the design is changed in appearance after the rescale event. When rescaling focal length, the diameter of the surfaces is not changed. Note that the other rescaling choices (1) to rescale on diameter and (2) 'Both'. In case (1), all surface diameters are changed in proportion to the new value to be assigned to Surf #1, and all other surface parameters are unchanged. In case (2), both diameter and focal length are changed in proportion to an entered scale factor. You would select <Edit><Rescale><Both> to convert, for example, a 50 mm f/4 lens to a 80mm f/4 lens. You should know that it is possible to rescale to an inadmissible design. For example, if rescaling to a diameter that is too large, "negative" edge thicknesses could result. This will yield unpredictable results. Reduce the displayed size of the Rx by selecting <View><Zoom Out> and Save (<File><Save> or CTRL-S).
Right-click in the Reference field and select <Rx Reference><Edit>. In the previous lesson, we made an entry in the Reference field by typing directly in the cell. Long text entries will 'wrap' within the field cell and may sometimes be more easily entered into the input box that opens. Type 'http://skyscientific.com' or any other URL and click 'OK' to place the text in the cell. Right-click in the same cell and select <Rx Reference><Open>. If you have an internet connection, the web page will open.

LESSON #4. The purpose of this lesson is to perform some ray tracing and examine the trace results.

In Lesson #1, we worked with a doublet design "AO1". Locate this design once again and make it the Current Rx. Although not always apparent, traces have been performed in the background throughout the previous lessons. A paraxial ray trace is performed each time the design is redrawn in the Graphics Window. It is from this paraxial trace that the focal length of the design is computed.
We can see direct evidence of the paraxial trace by changing the design wavelength [Design nm]. Select different spectral lines from the drop down box and observe the change in focal length appearing in the Rx Grid for "AO1". You may also enter a custom wavelength (between 200 and 2,000 nm) into the [Design nm] drop down box. The program will determine approximate refractive index data to perform the traces. Key-in '632.8', wavelength for a Helium-Neon laser. After entering a custom wavelength instead of selecting a spectral line from the drop down box, you must select <View><Refresh> to compute and display the focal length for the custom wavelength. Now select '587.6 Helium d' in the 'Design nm' drop down box.
Select the <Trace> Menu Command and note the changes appearing on the Design Form: (1) the background of the Graphics Window has changed from white to black. (2) The Rx Grid has been replaced with a table of design and aberration data results with blank fields for the Current Rx. (3) A [Zone] textbox shows up on the form with the default zone value = .707. The [Zone] indicates the fraction of the semi-diameter at which zonal traces for Zonal Spherical Aberration and Chromatic Aberration will be performed.
Now select <Trace><Axial & Oblique> to trace a pair of marginal rays and display the results. The center columns of the table show aberration name, achieved value and the tolerance value. If the achieved value is within the tolerance, the background for the value is green, otherwise it is red. Try selecting different wavelengths from the [Design nm] drop down box and note how the aberration values change. If you select <Trace><Options> you will be able to see what wavelengths are currently being used for the 'Blue' and 'Red' traces for Chromatic aberration. You may select a different pair of spectral lines here. This selection impacts only the current design. It is possible to clear the traces and redisplay the design only in the Graphics Window by selecting <View><Refresh>.
We will now trace an oblique ray (at an angle to the optical axis). Click on the [Object Angle] textbox and Key-in '2' for "2 degrees off-axis". Then reselect <Trace><Axial & Oblique>. Note that many of the off-axis aberrations such as Tangential Coma and Field Curvature are now showing non-zero values. Note also that an additional set of rays are drawn, representing the off-axis rays. Trace calculations are performed for all available traces, but you may control the rays which are drawn in the Graphics Window by selecting <Trace><Options><Draw Rays> and checking or unchecking the choices. "Oblique" rays are never drawn if the Object Angle and Object Height are zero. The 3 rays drawn for oblique traces represent the Upper Rim Ray, Chief Ray and Lower Rim Ray.
So far, we have examined designs with an Object Distance set at negative infinity (-INF), but we are able to specify a finite object distance. To see this, we will first pick a different design. Select <View><db View> to redisplay the Rx Grid. Now find the 'Cooke Triplet' design and make it the Current Rx. Change the '-INF' object distance to '-20', then select <Trace><Axial & Oblique> to see results at the shorter object distance. Note that at this closer object distance, marginal rays are unable to strike Surf #5 so that the program will reduce the ray angle until a ray is able to pass through the system. Also note that Effective Diameter shown in the table is less than the full diameter of Surf #1. When the object or image points are outside the Graphics Window, it is possible to select <View><Zoom Out> (or Press F12) to redraw the design and subsequent traces at a reduced image scale. Press the F12 key until both the object and image points are displayed. To trace from an extra-axial image point, note that because we are at a finite Object Distance, that [Obj Height] rather than [Obj Angle] should be non-zero. Click on the [Obj Height] field and key-in '4' for "4 inches above the axis", then select <Trace><Axial & Oblique> once again to see the results. Note also that a graphic representation of the object and image are drawn. This is done only for finite object distances with non-zero object height.

LESSON #5. The purpose of this lesson is to show how the program generates spot diagrams and encircled energy plots.

Select <View><db View> to restore the Rx Grid.
Make "Double Gauss" the Current Rx (this is a Double Gauss photographic lens design).
Select <Trace><Axial & Obliquie>, then <Trace><Spot Diagram>. Click on one of the four "positions" shown to draw the spot diagram at that "position". <Other> means that you will specify the distance from the last surface of the design at which to spot diagram is to be displayed. Select <Paraxial Image Plane> to show the 1250-ray spot diagram at the paraxial image plane from an axial image point. Now select <Trace><Spot Diagram><Number of Rays><2000> to increase the number of rays for the spot diagram and select <Trace><Spot Diagram><Paraxial Image Plane> once again to redraw the spot diagram. The centroid of the spot is shown by the short vertical bar on the top side of the measurement scale. Select <File><Print> or 'CTRL P' if you wish to print the spot diagram.
Now select <Trace><Spot Diagram><Encircled Energy> to view the "Encircled Energy Plot". Note that about 70% of incident rays will image within a circle of radius = .15 inches at the specified wavelength.
Select <Trace><Spot Diagram><Polychromatic> to check that menu item. When checked, spot diagrams are generated for 3 color wavelengths: the current design wavelength plus the wavelengths selected for the chromatic traces. Then select <Trace><Spot Diagram><Paraxial Image Plane> to display results.
Select <View><dbView> and locate the design 'Folded Refractor'. Select <Trace><Axial & Oblique>, then <Trace><Spot Diagram><Resolution (Double Star) Test>. This feature simulates the ability of the optical system to resolve two point sources at infinite distance, with a specified angular separation. In the dialog box which opens, you are advised of the theoretical minimum angular separation that an optical system of the current aperture is able to resolve. Accept the default value and click [OK]. The plot shows the two point sources at 1.21 arcsec are not very well resolved at the paraxial image plane. Now select <Trace><Spot Diagram><Show Airy Disk>. With this menu item checked, spot diagrams and encircled energy plots will indicate the Airy Disk on each plot. Select <Trace><Spot Diagram><Resolution (Double Star) Test> once again to display the circle representing the size of the Airy Disk.

LESSON #6. The purpose of this lesson is to understand how tilted surfaces may be used in your designs.

Select <View><db View> to restore the Rx Grid and select 'a new lens'. This is a design that we created in Lesson #2 and modified in Lesson #3. Expand the Detail Grid and select Surface #3. Select <Delete><Train> from the <Edit> menu to delete all surfaces after the first element.
Select Surface #2 in the Detail Grid and select <Edit><Insert or Append><Surface> and complete the remaining fields with Medium = 'MIRROR', Diameter = '40', Distance = '100', leaving Rc = 0. Clicking in the plot area will display the Rx, now with 3 surfaces. Select <File><Save> or CTRL-S to save the design. Then perform an Axial & Oblique trace. Now try entering some non-zero values in the Tilt field for Surface #3, selecting <Trace><Axial & Oblique> after each change. Note that up to about 65 degrees, the marginal rays are still able to strike the mirror. Note also that none of the calculated design parameters change, as the flat mirror does not impact the aberrations of the system. Entering an angle of 75 degrees will result in a reduction of the effective diameter of the system. The largest angle that may be entered is +/- 89 degrees.
With the tilt angle of Surface #3 at 30 degrees, try changing the Object Angle of the design. Select <Trace><Axial Oblique> after each change.
Once tilted surfaces are introduced into a design, the coordinates displayed in the [X-Val] and [Y-Val] fields may no longer provide measured distances of interest. However, you are able to measure any vertical, horizontal or diagonal distance between any two points in the graphics window by successively right-clicking on the two points. Try it.

LESSON #7. In this lesson, we will change some defaults and settings for the application design.

Select <View><Defaults>. This opens the Defaults Form which controls initial settings for new designs as well as other defaults.
Change the [Units] to 'in'. This will specify the units for new designs when <File><New Rx> is selected.
Change the [Object Angle] to '1'. Then close the form. These changes will result in New Designs using 'inches' instead of 'mm' and set the Object Angle at 1 degree. You will need to close and restart the program for these changes to take effect.

LESSON #8. In this lesson, we will create a design, evaluate it, and then use the XY Plot feature to improve the design.

We want to design 3" diameter f/15 achromatic doublet using Acrylic and Polystrene plastics. If we were to look at the Glass Catalog (try this by selecting <File><Open Glass Cat> we would find V-values of 57.2 for ACRYLIC and 30.8 for POLYSTYRENE. Now close the Glass Catalog.
We know that a positive and negative combination of two lenses will be nearly achromatic if the focal lengths vary inversely with the V-values. That is, an ACRYLIC lens of 30.8 inches focal length combined with a POLYSTRENE lens of -57.8 inches should have a fairly good color correction. We shall also use the fact that an equiconvex (or equiconcave) lens has a focal length nearly equal to the radius of curvature if the refractive index is near 1.5 . Our end goal is a final design that is within tolerance limits for LA' , OSC and Chr'.
Select <File><NewRx> and enter the 'Plastic Doublet' as the Rx Name. Note that the units of measurement for this new Rx is 'in' for 'inches'. Change [Type] for Surf #1 to 'Sphere' and enter the following for Surface 1: [Medium]= 'ACRYLIC', [Diameter] = '3', [Rc] = '30.8'. Then click near the center of the Graphics Window to set the position of Surface #1. For Surface #2. enter 'Sphere' as the [Type], [Medium] = 'AIR' and [Diameter] = '3'. Enter [Distance] = 0.4 and [Rc] = '-30.8', then click in the Graphics Window to redraw the lens. Now Save the design.
We will now create a separate new design for the 'flint' (POLYSTYRENE) element. Select <File><NewRx> and name the lens 'Poly1'. We want the final design to be a contact achromat so for this lens enter [Type] = 'Sphere'. In addition to simply typing in a Medium Name, it is possible to make a selection from the Glass Catalog: Double-click in the [Medium] column. After the Glass Catalog opens, find the record for 'POLYSTYRENE', highlighting it. Then close the Glass Catalog Form. The [Medium] column should now contain the correct medium name, 'POLYSTYRENE'. Now complete the remaining surface details: [Diameter] = '3', [Rc] = '-30.8'. Then click near the center of the Graphics Window to set the position of Surface #1. Then enter for Surface 2: [Type] = 'Sphere', [Medium]= 'AIR', [Diameter] = '3'. We need to select a radius for Surface 2 such that the focal length of this element is about -57.2 inches. Let us guess a value [Rc] = '-100' and also enter [Distance] = '.3' . Update the Graphics Window, then Save the design.
In the Rx Grid, note that the focal length for Poly1 is now displayed as -75.56. This is weaker than the desired value of about -57.2, so let's make the rear surface flatter to increase the strength of this lens and get closer to the -57.2 value for focal length: Change [Rc] for Surf #2 to '-200' and click on the Graphics Window'. Now the focal length is about -61 inches and we will consider this to be close enough, so save the design. CTRL-S is the shortcut to save.
Make 'Plastic Doublet' the Current Rx once again. We will append the Polystyrene element to 'Plastic Doublet': First click on Surf #2 in the Rx Detail Grid. Then select <Edit><Insert or Append><Library Item>. Click 'OK' in the dialog box, then locate and click on 'Poly1' in the Rx Grid. Click 'Yes' to append to the design and 'No' in the move dialog as we have no need to separate the elements. This completes the append operation. Note the focal length of the system of both lenses is about 63 inches.
As mentioned above, we actually want a zero air-space between elements. We could leave the [Distance] for Surface 3 at 0. Instead, we will simply delete Surface # 2: Click on the Surface Record #2 to make it the Current Surface, then select <Edit><Delete><Surface>.
A 3" f/15 design has a focal length of 45 inches. We want to reduce the system focal length to this value. Select <Edit><Rescale><Focal Length>. In the dialog box that opens, enter '45' and click 'OK', then press CTRL-S to save it.
We now have a 3" f/15 design, but we don't know how well this lens will perform. To find out, select <Trace><Axial & Oblique> and look at the table of aberrations and values that appear. It is interesting to note that while we made an effort to correct Chromatic Aberration (Chr'), it is well above tolerance. Meanwhile, Spherical Aberration (LA') was left to itself and came out quite good! Let us see if we can correct Chr' without killing our good spherical correction: We will do this by using the XY Plot function to vary R(2) over a range, automatically recalculating the aberrations at each point.
Make Surface #2 the current surface in the Rx Detail Grid, then select <XY Plot><X-Axis> and note that R(2) is checked. This is the X-Axis parameter (the "dependent" variable). Now select <XY Plot><Range><Fifty%>. This will tell the program that we want to vary R(2) from the current value of -21.7 inches over a range of +/ - 50%, that is, from about -33 to -10. Now select <XY Plot><Plot> to call the calculation routine and plot results. When asked if we want to maintain constant curvature for the current (Surf 1-2) element, click 'No'. This because maintaining constant curvature would tend to maintain the current state of Chromatic correction--and we want to correct it; not maintain it. The data plot appears in red with the current value of R(2) shown by the short red vertical line. The first plot is for LA'. Press the F8 key until the Chr' plot is displayed. The horizontal gray line corresponds to Chr' = 0, so the point where the red curve crosses the gray line is where Chr' is minimized. We could therefore improve Chr' by resetting R(2) to about -28 inches. We can do this now by simply clicking on the intersection of the horizontal gray line and the red plot line. Click 'OK' in the dialog box which opens and 'OK' again to restore the original focal length. Note in the aberration table that Chr' is now within the tolerance value. Moreover, while we have degraded the spherical correction somewhat, LA' is still within tolerance. Select <View><db View>. change and select <File><Save>. We have achieved the stated goal for this design so we can consider the job done. Now would be a good time to delete 'Poly1' as it is no longer needed. Make 'Poly1' the Current Rx and select <File><Delete>.

LESSON #9. In this lesson we will retrieve another design from the database to further demonstrate the XY-Plot function as well as a review of the editing feature.

In database view, locate the design 'SphericalCass' and select it to make it the Current Rx. This design is a type of Cassegrain telescope, but with spherical surfaces on both the primary and secondary mirror. In this case, there is a further simplification in that the primary and secondary have equal curvature radii. For the amateur telescope maker, this feature offers the additional advantage that the tool used to make the primary could be polished and reduced in size to serve as the secondary mirror, saving some of the work required to make an alternate secondary mirror. The disadvantage is that the secondary must be larger than the usual case for a Cassegrain telescope, obstructing more of the incoming light; in this case, about 21%.
For exercise purposes, let us first add a right angle prism to deviate the beam by 90 degrees after passing through the hole to be made in the primary: Make Surface 2 the current surface, then select <Edit><Insert or Append><Library Item> and choose 'RA Prism 28mm' to append to Surface 2. The program will initially place the prism at the vertex of the secondary, but we can move it with a click. Place it behind the primary. The [X-Val] field displays distance from Surface 2. Click where [X-Val] is equal to about 18. At this point, your graphics window should look like this:
Save the design, then select <Trace><Axial & Oblique>. The aberration table shows that Spherical Aberration (LA') is at over 3 times the tolerance value. It is interesting to note that the prism introduces a negligible amount of Chromatic error to what would have been zero for an all-mirror system. The Chromatic error is of no concern. We will attempt to improve the spherical correction by aspherizing the primary.
Change the Surface Type for Surface 1 from 'Sphere' to 'Ellipse' by typing an 'E' in the cell. When a non-spherical conic is entered as a surface, the program temporarily resets the Eccentricity value to 1, which is eccentricity for a parabola. For now, reset it to zero and repeat the Axial & Oblique trace. We will next use the XY Plot feature to vary the eccentricity of Surface 1 over a range in order to find the value that will minimize LA'.
With Surface 1 as the Current Surface, Select <XY Plot><X-Axis>< Ecc(1) >. Then <XY Plot><Range +/-><Min-to-Max>. Click <XY Plot><Plot> and enter the range for eccentricity values to plot from zero to two as ' 0 , 2 ' and click OK. Noting the [X-Val] field as you move the mouse cursor to the point where the red plot line crosses the gray line representing LA' = 0, we see that a value of eccentricity of about 0.72 should yield the desired result. We can get a more precise value as follows: CTRL-X will toggle between disable/enable autoscaling of the X-Axis. Disable it. Then select <XY Plot><Plot> and enter the new range as ' 0.7 , 0.75 ' and click OK. We can now identify 0.716 as an optimum value for eccentricity. Click on the graph at that point. Follow the prompts to reset eccentricity and restore the original focal length and observe that the aberration table shows that our design is much improved, so save it.
Figuring a mirror from a sphere (ε = 0) to an ellipse with a specified eccentricity is not easy. Mirror makers familiar with the Focault Test may know that the usual test may be modified by placing the point source at one focus of the ellipse and the knife-edge at the second. A "null-test" result means you have achieved the desired surface figure. Let's use the XY Plot feature of dbOptic to find the foci for the elliptical primary mirror:
In dbView, make a copy of the current design and name it 'Elliptical Primary'. Make Surface 2 the current surface and select <Edit><Delete><Train> to reduce our design to just the primary mirror. If our mirror had ε = 0 (spherical mirror) we know that LA' = 0 where the object distance equals the radius of curvature, in this case about -53 inches. For our elliptical mirror, we will guess that we can find one of the foci at some closer distance--somewhere between -50 and -30 inches. Select <XY Plot><X-Axis><Obj Distance>, then select <XY Plot><Plot> and enter the range ' -50 , -30 '. Viewing the plot, we see that the curve crosses the LA' = 0 axis at about -30.9 inches. We click at that point, verifying the result and noting that the image distance L' is about -186 inches, the position of the second focus of the ellipse. Of course, a knowledgeable geometrician could have calculated the foci from the expression R / ( 1 ± ε ) or -186.7 and -30.9, the same results that we found from the <XY Plot> function.

LESSON #10. In this lesson we will retrieve a different lens from the database and use it to demonstrate the meridional ray plots. For an interpretation of the shape of the curves, see the optical design primer.

Make 'Projection Lens' the Current Rx and verify that the design wavelength is set for the Helium d line, 587.6 nm.
Set [Object Dist] = '-INF' and [Obj Angle] = '0' (degrees).
Select <Trace><Axial & Oblique>.
Select <XY Plot><H' - TanU'> to display the plot. The short vertical bar on the plot corresponds to the Chief Ray. Try selecting different wavelengths from the [Design nm] drop down box and observe how the curve changes shape.

LESSON #11. In this lesson, we will explore spot diagrams for extended objects. In the spot diagram feature of this software, we trace from 300 to 2,000 rays through an optical system from a single point source. For the Double Star test, the source is two points separated by a specified distance. In the case of extended objects, there may be several thousand point sources. Naturally, a large number of object points will increase computation time.

From the Rx Grid, find 'Parabolic Mirror' from Lesson #8 and make it the current Rx. Select <Trace><Axial & Oblique> to display the trace results. Then <Trace><Spot Diagram><Paraxial Image Plane> to display the spot diagram from a single object point 3 degrees off-axis. At this angle off axis, note that the f/1 mirror exhibits considerable coma. Now select <Trace><Extended Objects> to display the Extended Objects Form and the Object Map. The Object Map is a 41 x 41 cell grid which may be used to create an extended object. Click on any cell in the grid to place an object point. Clicking again will remove it. Note that the axes of the grid correspond to the field width (Object Angle) for the design. Create a pattern by clicking on about 8 to 10 cells, spaced nearly evenly from left to right in a single row near the vertical center of the grid. Then select <View><Image> from the Extended Objects Form Menu. After processing, the resultant image at the Paraxial Image Plane is shown (a different plane could be displayed by selecting another plane and tracing a standard spot diagram before opening the Extended Objects Form). Note the effect of coma as the point sources are further from the center of the field. This object map may be saved and reused by selecting <File><Save> and entering a file name for the .DAT object file. There are a few example .DAT files in the \Images subfolder at the install location of this application.
We can also use a graphic file for the object with certain restrictions: The graphic object file must be a 256 color (8-bit) .PCX file with width and height in pixels exactly equal to each other. There are some example .PCX files in the \Images subfolder. We will be using the Jupiter.PCX file as our object. This file has 101 lines (pixels) of resolution. You may view it by opening the file with an imaging program such as MS Paint which comes with your Microsoft Windows® software. The 3 degree half-field currently set for our design is much too large for our object: The Jupiter file covers a true angular field of about 0.02 degrees, so we must close the Extended Objects Form and reset the [Obj Angle] on the design form to half of this value or 0.01. Then perform another Axial & Oblique Trace by selecting <Trace><Axial & Oblique> and then select <Trace><Spot Diagram><DLC>, and reopen the Extended Objects Form. Note that the range on the Object Map is from - 0.01 to + 0.01 degrees.
Now select <Open Trace From . . . ><Object PCX File> and browse in the dialog box to find the \Images subfolder at the install location, open it, and select the Jupiter.PCX file and click 'Open' to process and display the resulting image. With this particular selection of our design, object angle and object file, the application first determined that the size of our mirror was large enough to resolve the 101 lines in the original object file. If this were not the case, the application would have reduced the resolution of the object file by performing a merge operation, combining cells, until the 101 lines in the original file were reduced by a factor of 2, 3, 4, or 5 until the theoretical resolution of the design was greater than the number of lines in the virtual file. Repeating this exercise for our 3 inch diameter plastic doublet will demonstrate this process. A status message on the bottom left of the form indicates the current image plane and pixel size in degrees or linear dimension of the source object before any resolution reduction.
Select <View><Options> and uncheck the Autoscale Image. Reset the scale value in the upper left corner of the form to 0.05 and then select <View><Image> to display a slightly larger image. Any black "square grid" that may appear in the image is an artifact due to the resolution of your monitor.
If you wish to see how a larger and higher quality optic might perform on the same object, you could repeat the above steps using the 'Ritchey F/6' design.

LESSON #12. This lesson will assist you in applying the filter features to the dbOptic database. With only a few designs in the database, you will find little benefit from the filter capabilities, but as you add designs of your own or from the optional dbOptic Lens Library A (over 2,500 lenses, mirrors and systems from major optical suppliers) the benefits of the filter feature will become more apparent. As an example, if you had a large lens database, you could filter it in search of all lenses that were 25mm in diameter and had a focal length of less than 100mm.

Filter features are accessed from (1) <View><Filter> Menu Command or (2) right-clicking on the dbOptic Rx Grid.
Right-click on the Rx Grid and then use the left mouse button to select <Enter or Reset Filter>. A filter dialog opens which provides examples of filters you may enter and a text box where you may enter the filter expression. The default entry is 'Reset', which has the effect of removing all filters.
Try out one or more of the example filters by typing the filter string in the text box. Reset between trials. Note that you can see a count of the number of records in the filtered database simply by resting the mouse cursor over the Rx Grid after applying the filter. Use the 'Reset' feature to restore the unfiltered database.
Find the design 'BiConvex Lens w/RA Prism' in the Rx Grid and make it the current Rx. Using the left mouse button, click one or more times in the 'Description' column for this Rx until you see the vertical text cursor line. Click once more in front of the word 'Lens' to place the text cursor there, then hold down the mouse button and drag to the right until the word 'Lens' is highlighted (selected). Making sure that the selected text remains highlighted, click with the right mouse button anywhere in the Rx Grid and then left click the option < Filter by selection 'Lens' >. Note that our database of records has been filtered so that only those records with the word 'lens' in the description field are displayed.
Now find the record in the filtered Rx Grid with the word 'Camera' somewhere in the description field. Highlight the word 'Camera' then right click and select < Filter Excluding Selection 'Landscape' " and note that the list has been reduced by the excluded design.
In the above two operations, we applied two filters sequentially: First we reduced our database to those designs that had the word 'Lens' in the Description column, then we reduced further by excluding lenses that were described with the word 'Camera;. The filters are applied cumulatively until 'Reset'. Right click on the Rx Grid and select <Enter or Reset Filter> and reset.
The 'filter by selection' and 'filter excluding selection' features may be applied to the "Name", "Description", "Mfg" and "Reference" columns of the Rx Grid.

LESSON #13. This lesson will demonstrate the use of the <File><Link> feature in dbOptic. The Full-Feature License Version of dbOptic is required to demonstrate this procedure.

Open your 'My Computer' file system on your PC and browse to the folder where the dbOptic program is installed. If you installed at the default location, this would be on your computer C-Drive in the "Program Files" or "Program Files (x86)" folder. Open the folder marked 'dbOptic' and the data file 'dbOptic_data.LGF'. Right click on the file icon and select 'Copy', then close this window and right-click on your Desktop to 'Paste' a copy of the file there. Rename the file as 'dbOptic File 2.LGF'
Start dbOptic. Select <File><Link>. A message box will open showing the data file to which the application is currently linked. Click 'OK' to link to an alternate file. In the 'browse' window that opens, locate the file that we renamed on the desktop and click 'Open'.
You are now linked to the alternate file. It is easy to see how you might have several different optics data files on your PC. You can quickly change the application link from one data file to another.

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