Copyright © 1999 - 2020 Sky Scientific
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).
The purpose of this lesson is to gain familiarity with features and controls on the primary design screen of the program.
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 [+].
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
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.
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
<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
- 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
<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
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
- 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
- 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
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
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
- 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
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 &
- 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
- 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
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
- 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
- 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
- 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
End of Tutorial. Return to top of page.