I am going to discuss the different types of optical analysis which OSLO has available.  I will try to explain how to use OSLO.  I recommend the book Telescope Optics by Rutten and van Venrooij as a good place to learn about optical design and aberrations.  This book is published by Willman-Bell.

  I cannot take the time to explain all about each aberration or type of analysis.  But, I will comment briefly about several of these as they apply to an amateur telescope designer.  The spot diagram is probably the best overview of optical performance, but there are other important things to look at also.  Ideally all aberrations should be minimized, but often there are trade offs to be made.  I will try to comment on some of these.

  How good is good enough?  This question is not so easy to answer.  A lot depends on your priorities and what trade-offs you are willing to make.  The best way for an amateur to start answering this question may be to compare your design with another good design.  The atm_free Yahoo group has some good files in the OSLO sample files.  These are listed in the Files section.

  In general, a long focal ratio telescope will have smaller aberrations than a shorter focal ratio design.  There are exceptions to this, but it is true most of the time. For example, a short focal ratio refractor will have more color errors than a longer focal ratio design, if they are made from the same glass types.  One way to minimize chromatic aberration is to use more expensive glass types.  This is a trade-off that some people will make, but not everyone.  Part of the reason the more exotic glasses are expensive is that producing excellent quality glass is much more difficult.  And a refracting telescope objective lens needs to have very good quality glass in order to get good images.

  Let's start by making a refractor design.  This will be a 100mm f/5 doublet lens.  The glass types are available and relatively inexpensive.  This design would make a nice finder scope on your big telescope.  This is a fast focal ratio design, so there will be a lot of chromatic aberration.  A lens like this should work fine for low power observing, as would be the case for a finder telescope.  This design would not work as well for high power viewing as a 4" f/12 design.

  I have shown how to create designs in a previous OSLO How To page where I talked about data entry.  Please refer to these if you don't know how to set up a new design.

  I have entered a radius for the IMS, which is the image surface.  This will show better off axis images than a flat image surface would.  Refractor lenses suffer from many aberrations.  Field curvature at the image surface is one such aberration.  This is not normally a problem when used with an eyepiece.  Shorter focal length objective lenses have steeper image curvature, which causes more problems than longer focal length lenses.

  On the top right of OSLO is a window which says UW1, or it might say GW1.  This is the window we will use for analysis.  It looks like this:

These are the standard icons.

Each of the icons can be used to display different evaluation data.  You can evaluate many aspects of a design including a spot image and wave front errors - to name only a couple.  I will go over these briefly as we look at each type of analysis.

  Your UW 1 window might not look like my example, you might have different icons, or no icons except for the one in the upper left corner.  This can be changed by clicking on the icon in the upper left corner, which looks like a blue window with a red frame around it and a red cross through the center.  Clicking this will display a list of options.  The default option is shown in the image below, Standard Tools.  The Standard Tools will show 9 useful icons.

  I have moved my mouse cursor over the first icon.  Below the icon it displays a text box with a description of what this icon does.  It says, "Setup Window / Toolbar"    Left click on this first icon.

Now left click on the Standard Tools.  And your icons should look like mine.

Above I have shown the Standard Tools.  This Standard Tools option will be discussed on this page.  You have other options also, you might want to examine these later.  They will give additional options for a specific type of evaluation.  You can also see other options by clicking on the Evaluate button on the top tool bar.  There is a drop down window with many options.  These will not give icons in the evaluation window, they will open a window which shows the analysis you have chosen.  You can close this window when you are done with it, and this will return you to the standard OSLO windows.

Clicking on an icon in the UW1 or GW1 window will display an image in the window.  The second icon will display a drawing of the lens design.  This is the "plan" view, which is the first option.  It shows the lens with light passing through it on axis and off axis.  You will want to keep an eye on the edge thickness of the positive lens when you are working with a design.

The third icon is another drawing display which is a three dimensional drawing.  I don't use this much.

The fourth icon from the left will display a graphics ray analysis.  This has some very useful information.


  There are a couple of valuable things here, astigmatism, longitudinal spherical aberration, and chromatic focal shift.  When comparing different designs with each other you will want to pay attention to the scale used on each aberration.  A graph may look better, but it may be worse if the scale is bigger.

  Astigmatism is related to the field curvature at the image surface.  The IMS radius is set at -220 mm which balances the sagittal astigmatism and tangential astigmatism.  This would give the best images for this lens.  And it will give an idea of what the images would look like through an eyepiece.  A short radius on the IMS means that it would be hard to focus on the center of the field at the same time as the edge of the field when looking through an eyepiece.  Most refractor designs have an IMS of about 1/3 of their focal length.  Notice the image scale when comparing different designs.

  Longitudinal spherical aberration shows the spherical aberration at three colors (wavelengths).  Objective lenses which are optimized for visual use will have green light well corrected (0.588 micron or 0.546 micron wavelength).  The other two colors will normally have more longitudinal spherical aberration than the primary wavelength.  Most designs will balance the red and blue wavelengths against each other, as in this design.
  If you examine this same design using other wavelengths the errors will be different.  Each color has a different amount of spherical aberration.  The violet light will have the most deviation in this design, as in most designs.
  Objective which are optimized for photography will correct violet and blue light better than a visual optimization.  Violet light is more important in photography than in visual use.

  Chromatic focal shift shows where the different colors come to a focus.  The vertical scale show the wavelengths, 0.4 on the bottom is violet, and 0.7 on the top is red.  The horizontal scale shows the focal position for different wavelengths.  The violet light (0.4 microns) focuses about 2.3mm farther away from the lens than green light of 0.588 microns.  Red light (0.7 microns) focuses about 0.6mm behind the green light.  This color balance is typical for a visual objective lens.

The fifth icon shows a wave front analysis.

  P-V is peak to valley error.  RMS is root-mean-squared error.  In the above example the off axis evaluation is on the left side, while the on axis evaluation is on the right side.  This analysis is in the primary wavelength 0.5876 microns.  The on axis error is a little over 1/4 wavelength P-V, which is about 1/10 wave front error RMS.  These errors are wave front errors, not errors on the glass.

  The lens design uses spherical lens surfaces.  The above wavefront errors are based on perfectly spherical lens surfaces.  So, we are not looking at errors due to a defective surface on a lens.  These errors are based on a perfect lens of the listed design.  If the lens surfaces are not perfectly spherical then the wavefront errors will be different.  In most cases the errors will be worse.

The sixth icon shows a spot diagram analysis.

  This is the best overall evaluation for a quick check of image quality, but it may not be enough by itself.  For example, it is possible to have a good spot diagram even if there is more warfront error than desired.  And sometimes you may make the spot diagram look better without really improving the images.  So, it can be useful to check other analysis windows to double check the spot diagram.  Another good tool is the Strehl ratio, which I will explain later on this page.

  The above image has 15 spot diagrams.  The top row shows the spot diagrams for an off axis image which is 2 degrees away from the center.  The bottom row shows the spot diagram for images on the axis.

  The columns show a focus shift.  This means that the column on the left is 0.1mm inside of focus.  The column on the right is 0.1mm outside of focus.  The center column is at the current focus.  You can examine the spot diagram at any focal position you want.  For visual use a lens is normally focused for the primary wavelength because our eyes are very sensitive to green light, and less sensitive to blue and red light.  But, you might want to examine a lens which is focused for polychromatic light, which would be a balance of all three wavelengths.

  A little later on this page I will explain how to display the Airy disk in the spot diagram analysis.  The Airy disk is the black circle in the center of the spot diagram.

The seventh icon displays a point spread function analysis.

  The left column shows a three dimensional view, while the center column shows the same data in a two dimensional diagram.  The bottom graphs in these two columns show the on axis analysis.  The top graphs in these columns show the off axis analysis.  The on axis image is much better than the off axis images.  The sharp spike is very good, a wide blur is not as good.
  This graph shows how much light is focused near the center of the image, and how much light is spread out.

The eighth icon displays a modulation transfer function analysis.

  Modulation transfer functions give an idea about how much contrast a lens will be able to show.  On the top of this graph is a black line with small circles through it, this is the ideal value.  A very good lens will come close to this line.  A fast focal ratio lens will perform worse than a long focal ratio lens - if they both are made of the same kinds of glass.  Expensive glass types can give better images than normal glass types.
  The purple line with the crosses through it show the on axis values.  The goal is to get this line as high and close to the ideal line as possible.  The green line with the squares and diamonds through them shows the off axis values.  Ideally both these green lines should be as good as the on-axis line.  And they should be balanced with each other so they are close together.  It is not as good if one green line is high, while the other green line is very low.  The above example is good considering the type of lens we have here.

The ninth icon displays a different modulation transfer function analysis.

  Again on the top is a line which shows the ideal value for this lens.  The three colored lines below it show the actual values for this lens on-axis and off axis.  This lens is a very good design for a fast achromatic lens.  You will notice that the off axis curved lines are spread out on either side of the on-axis curve.  This is good.  If you change the IMS radius you will see that the off axis curves will shift to the left or right.
  A better design will have these curved lines coming closer to the ideal line, they would be higher on this graph.  A good design will have the off axis curves just about as high as the on axis curve - as this design does.  A poorer design will have the off axis lines much lower than the on axis lines.


  You can add the Airy disk to the Spot Diagram Analysis.  The easiest way to do this is:

  Spot Diagram
    Single Spot Diagram

  Click Yes on the bottom left under Show Airy disk in plot.  Then click OK.

  The single spot diagram should now look like this.  The black circle in the center is the Airy disk. It is very small in this example because there is a lot of light spread outside the Airy disk.  At this point the Airy disk will appear in all the spot diagram analysis diagrams.

  The Airy disk shows the minimum size for a star image due to the wave nature of light.  OSLO shows spot sizes smaller than this based on geometric optics.  This can be a useful tool when designing and evaluating optics.


Click on   Evaluate
                  Other Aberrations
                      Zernike Wave front

This window will be displayed.  You have several choices, the image below shows the default values, which is minimum RMS and monochromatic.  You may want to select the Polychromatic option to evaluate how well the other colors are focused.

Below is the display of the Strehl Ratio.  A Strehl ratio of 1.00 is perfect.  Often Amateur telescope makers talk about Strehl Ratio of 98, this is like 98%.  The OSLO display will show Strehl as 0.98 instead of 98%

Our 4" f/5 lens has a Strehl Ratio of 0.67 for the primary color of light.  This is a monochromatic evaluation.

                                          DISPLAYING ITEMS IN THE TEXT WINDOW

  I have moved my mouse cursor over the highlighted abbreviation.  The text is displayed for several of the more useful data.  Left click on the Len to display the lens data.  This will display the current values for the file which is open.  This screen shot shows the display when the mouse cursor is over the Len area.

Special data (Spe) shows things like conic constants.

Refractive index data (Rin) shows the glass types in the current design.

Wavelength data (Wav) displays the current wavelengths.  These can be changed, I'll show this next.


  To change the wavelengths or add more wavelengths click on Wavelengths which I have circled in red.

  The window below will open.  Nbr 1 is the number 1 wavelength, this is the primary wavelength.  Normally it is 0.587 (d) or 0.546 (e) for a visual design.  The image below shows the default values.  You can add additional wavelengths also by clicking on a Nbr then on the blue arrow at the top right corner.  This will insert another wavelength row.  You may select the wavelength for this new row also.

  OSLO is set up to use number 2 wavelength as a shorter wavelength, and number 3 as a longer wavelength than the number 1 wavelength.  You can select any wavelength for the additional wavelengths.

  To add more wavelengths left click on a gray box under Nbr.  Then on the upper right corner you will click on the blue arrow icon.  This will add a new row above the row you started with.  After you add more wavelengths you will want to restore the order of the top three rows so they are like the original order when you started.  Number 1 is the primary wavelength (0.587 or 0.546).  Number 2 is the blue (0.486) and Number 3 is the red (0.656).  Numbers 4 and below can be any wavelength you want to use.

You can add several additional wavelengths, I like to add the "g" and the "h" voilet wavelengths sometimes.

You can change the wavelength.  You can enter a different value in the wavelength box, or double click on a wavelength and see a drop down window where you can select a wavelength.

  On the right of the wavelength is the weight.  This is the relative importance you place on these wavelengths.  1 is 100 percent weight.  If you have more than three wavelengths you might want to set the weight of these additional wavelengths at less than 1, say 0.2.  The weight will influence the optimization and some of the analysis results.  You might want to set the weights to the relative importance of the human eye, this will have 0.546 as 1, and 0.4 as very small, say a weight of 0.01.

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Steve Fejes