CODEV Ch6
CODEV Ch6
CODEV Ch6
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Chapter 5
Resist Murphy’s Law: Tolerancing
You are probably familiar with Murphy’s Law: “Anything that can go wrong, will go
wrong.” Tolerancing is an attempt to resist Murphy’s Law, by understanding what
sorts of errors can occur, how badly they will affect optical performance, and what is
the probability of building a system that works.
CODE V has a number of tools for tolerancing, including a powerful feature called
TOR. Other tools are provided for analyzing user-defined tolerance criteria and for
Monte Carlo simulations.
Contents
Murphy’s Law...........................................................................................................120
Tolerancing and TOR................................................................................................123
Tolerance Types ........................................................................................................125
Tolerancing with the LDM and TOR........................................................................126
Understanding TOR Output......................................................................................137
Other Tolerance Analysis Features ...........................................................................142
Murphy’s Law
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Optical systems require precision in fabrication. Errors that might be insignificant
in many mechanical devices can cause terrible performance problems in an optical
system. Yet errors will certainly occur, since nothing can be built perfectly.
Tolerancing is concerned with understanding the types of errors that can occur in
building an optical system, and in predicting their effects before anything is built.
You can’t beat Murphy’s Law, but you can limit your exposure by knowing what
can go wrong, defining the limits of the errors, and predicting their effects.
Compensators
An important aspect of optical assembly is the ability to make adjustments during
assembly to compensate partially for the accumulated and random set of errors that
have occurred in the fabrication and assembly. These adjustments are called
compensators. Anything that can be a tolerance can in principle be a compensator.
The most common compensators are focal shifts or other air space adjustments.
You will find that the selection of effective compensators is one of the most
important tolerancing tools, often transforming very tight (small) tolerances to very
reasonable values. Compensator selection requires some familiarity with possible
mounting methods, since there must be a physical means to accomplish the desired
shift over the required range.
Statistics
Unfortunately, there is no way to hold everything perfectly except for a single error.
In reality, all errors will occur simultaneously and randomly, although within the
assigned tolerance limits (you hope). This means there is no way to predict the
exact performance of a particular real lens built with a given set of tolerances. If
you build 1,000 lenses, each will have slightly different performance. The best you
can do is to predict the statistical distribution of the results. You can say something
like, “If I build 1,000 lenses, 980 of them will have a performance within 11% of
the nominal design.” If 11% degradation is acceptable, and if 98% yield is
acceptable, you are done. If not, then you need to do something—perhaps tighten
some tolerances, or provide some adjustment (a compensator) that improves the
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quality or yield. In the worst case, you may need to redesign the lens to be less
sensitive.
CODE V’s tolerance features (TOR and others) offer exactly these types of
statistical predictions, and allow you to change tolerances, adjustments
(compensators), and other assumptions in order to find solutions before hardware is
built.
Tolerancing Goals
The primary objective in tolerancing an optical system is to determine the
combination of dimensional ranges for fabricated elements which will minimize
manufacturing cost while satisfying performance, packaging, and appearance
requirements. It is an important part of the lens design process. The TOR option,
found on the Analysis > Tolerancing menu, has been developed to eliminate most
of the practical difficulties involved in tolerancing. TOR enables the designer to
concentrate on the optical system and its performance, rather than on extensive and
costly calculations and indirect results that may be difficult to interpret.
TOR Functions
TOR directly relates the manufacturing errors to measurable performance
requirements, either polychromatic diffraction MTF (at a specified frequency and
orientation), RMS wave front error, fiber coupling efficiency, or polarization
dependent loss. Four separate menu items access the four quality modes (MTF,
RMS Wavefront Error, Fiber Coupling Efficiency, and Polarization Dependent
Loss) all found on the Analysis > Tolerancing menu). TOR’s basic unit of
information is the change in the quality criterion (MTF, RMS wavefront, coupling
efficiency, or polarization dependent loss) caused by a parameter change of a
certain amount. This sensitivity calculation includes the effect of adjustable
parameters (compensators) specified by the user to simulate the assembly
procedures of focusing, tilting the image plane, etc., to maximize the performance.
Boresight (i.e., shift of line of sight) correction and distortion change output are
available as options.
In some of the following discussions we will occasionally use the term MTF drop
to describe a performance degradation due to manufacturing errors. You should
recognize that the discussion applies equally well to degradation in the other quality
criteria used in TOR, RMS wavefront error, fiber coupling efficiency, or
polarization dependent loss, depending on what you choose to use for your optical
system.
Interactive Tolerancing
After any initial TOR run, sensitivities are saved with the lens data so certain
subsequent tolerance analysis can be done more quickly (no ray tracing is required),
provided the lens data remains unchanged. Interactive tolerancing uses this saved
data to allow you to change tolerance values and immediately see their effects on
predicted performance. This is found on the Analysis > Tolerancing > Interactive
Tolerancing menu and can only be accessed after a standard TOR run has been
done (MTF, RMS Wavefront Eror, Fiber Coupling Efficiency, and Polarization
Dependent Loss).
If you are going to close the lens before using interactive tolerancing, you can save
it with Save Lens As. You can then restore the lens with the saved TOR coefficient
data and immediately use interactive tolerancing.
Tolerance Types
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CODE V supports many types of tolerances, a few of which are listed here.
Tolerances are considered to be part of the lens data and thus are defined and
reviewed in the LDM, as will be shown in the next section. Most tolerances are
linear quantities that are measured in lens units (most often mm). Angular errors are
measured in radians (this is different from construction data tilts and field angles,
which are measured in degrees). Not all possible tolerances are included in
automatically generated default sets; you can always add or remove tolerances from
default sets, using the Review > Tolerances menu. Some tolerance types have
special definitions. Here are just three examples of the many tolerance types.
Test plate fit (DLF)—A measure of the closeness of fit between a surface and a
reference test plate surface, measured as the number of interference fringes
(Newton's Rings). Irregularity (IRR) is also measured in this test, as elliptical
deviations from the nominally circular rings.
Wedge—When the front and rear surfaces of an element do not share a common
axis, the error can be described as surface tilt, or more commonly as a wedge,
described as TIR (total indicator runout), from the device and method of
measurement in the shop.
Barrel Tilts (BTI)—When a group of surfaces is tilted as a unit, this is called a
barrel tilt (in radians). Barrel tilts require a surface range, and the first surface in the
range is the default pivot point, though this can be changed with offsets in X, Y,
and Z.
Note: The only groups of surfaces that CODE V can recognize for default tolerance
purposes are single and cemented lens elements. Although other groups of surfaces
may form a group for construction purposes, CODE V does not know the mount
structure, and thus has no way to know that this is a group. For example, if you know
that surfaces 8 through 15 are a subassembly, you must add BTI S8..15 (and other
group tolerances) to the default set, or the errors of placement of this group will not
be simulated.
Starting on page 10-4 the CODE V Reference Manual has descriptions of all
available tolerances.
The lens is a Cooke triplet (f/4.5, 20° semi-FOV, 50 mm focal length). This
sample lens has no pre-defined tolerances.
2. Choose the Analysis > Tolerancing > RMS Wavefront Error menu.
The RMS wavefront error dialog box is displayed, with Polychromatic RMS
selected as the quality criterion.
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Setting Up Tolerances
Search As mentioned earlier, tolerances are actually considered to be part of the lens data,
and as such they are defined, viewed, and edited in the LDM. They are also saved in
the .len file when the lens is saved.
1. Choose the File > Open menu and locate the lens file cooke1.len in the
CODE V supplied lens directory.
This is the same predefined lens file that you opened in the previous procedure;
you need to reopen this lens file to ensure the correct results in this procedure.
2. Choose the Review > Tolerances menu.
The Tolerances and Compensators window is displayed. Note that this win-
dow is empty, since cooke1.len does not include any tolerances by default.
3. Click the Autofill button at the top of the spreadsheet to open the Tolerance
Spreadsheet Autofill dialog box.
The default settings (generate default tolerances for all surfaces) are good in this
case.
4. Click OK to define the tolerances.
The tolerances displayed in the Tolerances and Compensators window are
standard default values. Scroll down and notice that 53 default tolerances have
been generated for this six-surface centered lens. You could use right-click to
add (Insert) or remove (Delete) tolerances from this list. Every cell that is not
grayed-out is editable (e.g., double-click a Type item to change it to a different
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type).
Tip: To change the width of any columns in this window, right-click on a column
header and choose Column Width (120 works pretty well for the Type column).
No calculations have yet been done to see the effect of these tolerances (that’s
what TOR will do). You must still define a defocus compensator; once you start
to define tolerances and compensators, CODE V assumes you will define all
that you need, and nothing is generated automatically.
5. Right-click on the End of Data line in the Compensators spreadsheet at the
bottom of the Tolerances and Compensators window.
6. Choose Insert from the shortcut menu.
7. Double click the Start Surface cell and select Image surface.
8. Double-click the Type cell for this new compensator and scroll to locate and
select DLZ - Surface Z-Displacement as the compensator, as shown below.
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In the case of the image surface, thickness (DLT) and Z displacement (DLZ) are
equivalent, and you don't really need to change from the default value except as
a demonstration. In general, DLT changes the thickness by pushing back follow-
ing surfaces, while DLZ only shifts the surface, leaving other surfaces
unchanged.
9. Click the Commit button at the top, or click anywhere in the tolerance list to
commit the data for the DLZ Si compensator just defined.
10. Choose the File > Save Lens As menu to save a copy of the lens with the newly
defined tolerances and compensator.
5. Click the Quick Best Focus icon on the Quick Analysis tool bar:
Search This will run Wavefront Analysis option with the Replace Focus command,
analyzing the RMS wavefront error of the system and setting the image surface
defocus (THI Si) to maximize it. This is not exactly the same as optimizing the
MTF, but it's a reasonable approximation.
6. Re-run the MTF calculation by clicking the Execute button on the MTF
window.
Notice that the MTF curves are slightly improved. We will use 15 cycles/mm
as the tolerancing frequency. Note that the radial (0°) and tangential (90°) azi-
muth MTF curves for the off-axis fields are substantially different. You could
choose one of the azimuths for tolerancing (TAN is the default) though it is best
to include both. To do so requires duplicating the off-axis fields.
7. Choose the Lens > System Data menu and go to the Fields/Vignetting page in
the System Data window.
8. Insert two new fields into the spreadsheet on the Fields/Vignetting page. You
can insert a field by right-clicking over an existing field row and choosing
Insert from the shortcut menu. Once you’ve added two new rows, copy and
paste values from existing fields into the new fields (you can use the Copy and
Paste features in the Edit menu to do this). The result should be five fields, with
the field data matching what is shown in the following illustration.
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9. Choose the File > Save Lens menu to update the saved copy of the lens, which
will now include the tolerance definitions and the five fields (YAN 0 14 14
20 20).
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1. For Spatial Frequency, enter 15 in the Lines per MM field for all five fields.
2. For Azimuth, click in the initially blank Lines Orientation cell and use the
down arrow four times to create 5 field entries (or use right-click Insert).
Double-click the Field row and set row 2 to field 2, row 3 to field 3, etc. Change
the orientation from TAN to RAD for fields 3 and 5, as shown above.
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Tip: Although the limits only apply to the current TOR calculation, you can
enter the limits for your optical shop and use Option Set to save this as a
“template” for future TOR runs (you might call it “My Shop Limits”). Start
every TOR input by loading this option set, then modify other tabs as needed.
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Sensitivity Tables
There is one sensitivity table for each field (the 20° full-field is shown below, for
tangential MTF). The table starts with information about the number of rays traced
(always worth a look to check for problems) and the nominal performance at this
field point. This is followed by the long list of sensitivities.
You can interpret the sensitivity data in the following way (taking DLF S2 as an
example): an error of 2 fringes of power on surface 2 will cause a change of MTF of
+0.008 if positive, and -0.007 if negative. These changes assume that the
Note: There can only be one value for each tolerance and compensator, as you
can verify by comparing particular tolerance entries between fields. Each
tolerance will produce a different effect on each field, and in fact one field will
always be the worst case that determines the tolerance value in an inverse
sensitivity run.
Probable Change in MTF is a statistical value based on combining all the defined
tolerances. Additional statistics are printed at the end of each sensitivity table and
are explained below.
some cases. But the most common cause of this is the use of limits: TOR places
upper and lower bounds on all tolerances to prevent unrealistic values
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(microscopically tight or very loose). These limits are displayed in the text output.
The centered limits are shown below (note that the program also displays the limits
for decentered tolerances).
As discussed earlier, you can modify the limits on the Tolerance Limits tab in the
TOR dialog box. The TOR section of the CODE V Reference Manual (Chapter 22)
explains the factors that determine values in more detail.
• Cross terms are included in the statistics, i.e., errors can combine with or
partially cancel the effects of other errors.
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A table such as the one below is displayed for each field.
The interpretation of the cumulative probability table is that 97.7% of the systems
built will have a change in MTF of -0.054 or smaller from the design MTF for this
field, assuming the lens is built to the tolerances used in the lens model. The other
percentages can be interpreted the same way (50% represents the mean, while
84.1%, 97.7%, and 99.9% represent confidence levels of 1σ, 2σ, and 3σ,
respectively). The note on the right side of the table describes what is something
like a worst case, assuming that all parameters are fabricated at the extremes of the
allowable range.
Compensator Range
The probable change of compensator also approximates the 2σ level. This means
that if the compensator (focus shift in this case) can vary by ±0.5 mm, this range
will allow compensation for about 98% of the systems built (i.e., 2% of the systems
will have combinations of centered errors too large to be focused out by this range
of motion). This information provides guidance for mount designers as well.
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Supported
Tolerancing Supported
Algorithm Performance Comments
Method Tolerances
Metric
Polarization
Dependent Loss
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