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Chapter 7
Non-Spherical Surfaces

Many optical systems use non-spherical surfaces, including aspheres, cylinders, and
others. CODE V has a number of types available, including diffractive surfaces.

Contents

Non-Spherical Surface Types ...................................................................................158

A Non-Spherical Example........................................................................................160
Conic Surfaces ..........................................................................................................166
Entering an Ellipse....................................................................................................168
Polynomial Aspheres ................................................................................................171
Aspheric Singlet Example ........................................................................................173
Diffractive Surfaces ..................................................................................................177
Ray Grid Issues.........................................................................................................180

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Non-Spherical Surface Types

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Non-Spherical Surfaces
Non-spherical surfaces are widely used in modern optical systems. Conic sections
appear in many reflecting systems (including the common Newtonian telescope
with its parabolic primary mirror). Polynomial aspheres are becoming quite
widespread due to modern manufacturing methods such as glass or plastic molding
and numerically controlled methods such as diamond turning (modern diamond-
turning methods can directly produce precision aspherics on metal, glass, plastic,
and special materials such as germanium). Many infrared systems use aspherics,
and most optical disc systems use a doubly aspheric singlet for the disc-reading
objective lens. Diffractive optics have also become more common. Ruled
diffraction gratings have been used for many years in spectrometers and other
instruments. Holographic elements are used in some applications. Non-holographic
diffractives such binary optics are becoming more common.
CODE V has two classes of surfaces, rotationally symmetric and non-rotationally
symmetric. These are listed in the section below. In general, when using rotationally
symmetric surfaces, you can use Y-fields and circular apertures (maintaining
bilateral symmetry), whereas for non-rotationally symmetric surfaces you may need
to define multiple field or object points with X- and Y components, and use
rectangular or elliptical apertures.
Non-spherical surfaces are all identified by descriptive names in the user interface
and by a three-letter command code (SPH, CON, etc.), used in command inputs and
in many output listings. In this section, we will introduce several of the more
common surface types. Other types are defined and modified in exactly the same
way, although they will typically have more and different coefficients and
parameters defining them. Do a search in the Help or in the CODE V Reference
Manual for complete information on any special surface type (the three-letter code
is a good search string, although you can use other key words as well).

Rotationally Symmetric Surface Types

These surfaces include the following surface types:
• Sphere (SPH)—Spherical surface, including plane (zero curvature) surfaces.
The default surface type in CODE V.
• Conic (CON)—Pure conic (parabola, ellipse, or hyperbola).
• Asphere (ASP)—Polynomial aspherics, which are 20th order deformations to a
base conic surface.

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• Spline (SPL)—Spline surface (defined by four radial heights and surface

slopes).
Search
• Thermal gradient (THG)—Thermal gradient surface (normally created by the
environmental change feature of CODE V). It is actually an asphere that
simulates a thermally induced index gradient.
• Grating (GRT)— Linear diffraction grating ruled on a 10th order polynomial
asphere.
• Lens module (MOD)—Lens modules are black-box lenses used to represent
thin or thick lenses that are either perfect or have specified amounts of third
order aberrations (unique among special surfaces in requiring two adjacent
surfaces).

Non-Rotationally Symmetric Surfaces

These surface types include the following:
• Cylinder (CYL)—Cylindrical (has non-zero curvature and hence power only in
the Y-Z plane or the X-Z plane).
• Y Toroid (YTO)—Toroid in Y-Z plane, which is a 10th-order polynomial
rotated about a generating axis parallel to the Y axis.
• X Toroid XTO—Toroid in X-Z plane, which is a 10th-order polynomial rotated
about a generating axis parallel to the X axis
• Anamorphic asphere (AAS)—This surface has different curvatures and 10th-
order aspheric profiles in the X-Z and Y-Z planes (bilaterally symmetric in both
X-Z and Y-Z planes).
• Holographic/Diffractive (HOE)—All forms of general diffractive surfaces
(such as “binary optics”) are modeled with so-called holographic surfaces.
• User Defined (UDS, UD1, UD2, UD3)—User-defined surface, defined by a
user-written subroutine in Fortran or C, which is linked into CODE V.
There are additional non-spherical surface types available in CODE V called
special surfaces (SPS). They are different from the types listed above in that they
all share the command code SPS, with a qualifier word describing the specific type
(e.g., the Odd Polynomial is called SPS ODD, and includes terms for both odd and
even powers of radius, while the Superconic is called SPS SCN). They are listed in
the user interface as unique surface types, which of course they are. But when you
look at output listings you should understand that SPS ODD and SPS SCN (and
others) represent different types of surfaces. Do a search in the CODE V Reference
Manual for SPS for complete information.

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A Non-Spherical Example
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Flat-Field Schmidt
As an example of a system with a non-spherical surface, take a look at the CODE V
sample lens Flat-field Schmidt. This is a well-known catadioptric (reflecting and
refracting) design form. It has an aspheric glass element of very low optical power
in order to correct the spherical aberration of the spherical primary mirror, allowing
a fairly fast system (f/1.3 in this case). Field curvature is corrected by a lens element
very close to the image plane. We won’t do much with this example except look at
the user interface elements that you will use in working with all non-spherical
surface types.
1. Choose the File > New menu to launch the New Lens Wizard. Click the Next
button to go to the second page in the New Lens Wizard.
2. Select CODE V Sample Lens (default) and click Next.
3. Scroll down to find the file cv_lens:schmidt.len, and click on it.
4. Click the Next button on the remaining New Lens Wizard pages to view and
accept the system data values for the lens, or click the Finish button to accept
all values and view the lens.
5. Choose the Display > View Lens menu. In the View Lens dialog box, click
Hatch back of mirrors on the Lens Drawing tab, then click OK.
The lens picture is shown below (the label was added with text and line annotation
tools that are available in all graphics windows).

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Here is the LDM spreadsheet for this lens. Note the word Asphere in the Sur-
face Type column for surface 1 (stop).
Search

If you double-click the word Asphere on surface 1, you will see the following
list.

This is one way to change a surface to a non-spherical type. It is also handy for
changing to a sphere, which requires no additional data beyond the always-pres-
ent radius or curvature. But other surface types require additional data found on
the surface properties dialog.

Tip: Note that changing any special surface to a sphere throws away all the
special coefficient data (but you can always use Undo to get it back if you make
a mistake).

6. Right-click on the word Asphere on s1 and choose Surface Properties from

the shortcut menu.

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This will open the surface properties dialog at the appropriate page, as shown
below.
Search

On the Surface Type page, you can change the type of surface from the drop-
down list, and you can also change the values or the status (variable, frozen,
pickup, zoom) of any of the coefficients associated with the surface type (right-
click on the value of interest). These are shown in the spreadsheet to the right.
If you choose the Display > List Lens Data > Surface Data menu, a window is
displayed containing a text-style listing of all the surface information. The infor-
mation is listed in compact form labeled with the command names of the vari-
ous parameters. These command names are usually listed in the Surface
Properties window as well, such as Conic Constant (K). The command names
are usually derived from the variable name used in equations for the various sur-
face types, some of which you will see later in this chapter.

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How important is the aspheric surface corrector for this system? Take a look at a
spot diagram for the lens with and without the asphere.
7. Choose the Analysis > Geometrical > Spot Diagram menu. In the Spot
Diagram dialog box, click OK to run this option.
8. Zoom in on the resulting output with the magnifier icon and note the scale size
(it should be 0.05 mm).

9. Restore the scale (click the 1:1 button) and tear off a copy of the plot for later
comparison.
10. In the LDM spreadsheet window, double-click Asphere on s1 and select
Sphere from the dropdown list.
11. Click the Modify Settings button on the Spot Diagram output window you just
created. Click Aberration Scaling, enter 0.05 for the scale size, and click OK.
The Spot Diagram output window is regenerated.

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The before and after Spot Diagram plots are shown above. With the asphere, the on-
axis (zero field) RMS spot diameter is 0.0049 mm, while without the aspheric
corrector, the RMS spot diameter is 0.57 mm (shown on the Text tab of the Spot
Diagram output window).
It’s clear that a spherical mirror is not a good solution. Even with the corrector, this
lens is far from diffraction limited. Undo the sphere change and run the supplied
macro SPOTDET.SEQ (Tools > Macro Manager, in the Geometrical Analysis
category) and enter .05 for the scale and AIRY for the detector X width—you will
have to zoom in very close to see the circle for the f/1.3 Airy disk size.
Chromatic aberration is a problem for this lens due to the two glass elements
(note the separation of the red and blue light, especially evident in the classical
coma-shaped off-axis spot). Lack of such chromatic aberration problems is one
advantage of all-reflecting designs.

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A Note on Obscurations
Search You may have noticed that there is no central obscuration anywhere in this system.
Strictly speaking, this is a mistake, because the detector and field lens would block
the central 33% radial zone of the entrance pupil. This is not important for
explaining the user interface for non-spherical surfaces, but it would be important
for detailed analysis, especially for MTF and other diffraction-based analysis.
For the sake of completeness, here are the commands (used for brevity) to enter a
dummy surface to hold the required obscuration. Database items from CODE V are
used to show the logic of the calculation, but you could also calculate or estimate
the values by hand and insert the numbers in the spreadsheets. THI is thickness,
OAL is overall length, and SD is semi-diameter (default aperture radius). You can
type these commands at the CODE V prompt in the command window.

INS S3 ! insert dummy before S3

THI S2 (THI S2)+(OAL s4..i) ! distance to dummy
THI S3 –(OAL s4..i) ! dummy to primary distance
CIR S3 OBS (SD s5) ! obscuration size of final lens
SET VIG ! to correct reference rays for new apertures
VIEW ; HAT ; CAB ; GO ! make picture, including aperture ray
blocking (CAB)

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Conic Surfaces
Search
The conic surface is used to specify pure conics, such as parabolas, ellipses, and
hyperbolas. True conics are characterized by two foci; any ray passing through one
of the foci will pass perfectly through the other focus with no aberration. Conics are
defined by their conic constant k. The equation for a conic is given by the equation
shown below.

c( r2 )
z = ------------------------------------------------------ where r2 = x2 + y2 and c = vertex curvature
1 + 1 – ( k + 1 )c 2 r 2
k=0 sphere
-1 <k <0 ellipse
k = -1 parabola
k < -1 hyperbola
k>1 oblate sphere (not a true conic)

Ellipses
An ellipse, shown in the following figure, can also be defined by its major and
minor axes 2a and 2b. It is defined as the locus of points whose sum of the distances
from two points (foci) is constant. With the local coordinate system at the surface
vertex, the equation is given by

z – a ) 2- + ----
(----------------- r 2- = 1
a2 b2
The vertex radius of curvature is given by R = b2/a and the conic constant is given
by k = (b2 - a2)/a2. The distance between the two foci is 2F, where F2 = a2 - b2, and
the distance from the surface vertex to the foci is given by a ± F.

Foci

Surface vertex a
(radius R = 1/C)

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Hyperbolas
Search A hyperbola, shown in the following figure, also has major and minor axes a and b,
and is defined as the locus of points whose difference of the distances from two
points (foci) is constant. The equation can be given as

( z – a )2 r2
------------------ + ----- = 1
a2 b2

The radius of curvature is R = b2/a and the conic constant k = -(a2 + b2)/a2. The
distance from the center of the hyperbola to the foci is c = (a2 + b2)1/2 with the
distance from the surface vertex to the foci given by F = -a ± c. The hyperbola
curves extend to be asymptotic to lines at ±θ from the Z axis. The conic constant k
can also be given by k = -(1+tan2θ). As such, a cone can be approximated in
CODE V by a hyperbola with an appropriate conic constant and a very small radius
(e.g., 0.000001).

b
Z

Focus

Surface vertex
(radius R = 1/C)

Parabolas
A parabola is a degenerate ellipse or hyperbola with one of the foci being at
infinity. It is defined as the locus of points whose distances from a point (the focus)
and a line are the same. Since the conic constant is k = -1, it is described by an exact
second order equation, given by the following, where R is the vertex radius of
curvature and F is the focal length (F = R/2).

r 2- = -----
r 2-
z = ------
2R 4F

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Entering an Ellipse
Search To show how these equations are used, you can enter an ellipsoidal reflector with a
major axis of 100 (a = 50) and a minor axis of 60 (b = 30). Using the equations from
the previous section, you get the vertex radius R = 18 and the conic constant k = -0.64.
The distance from the surface vertex to the foci is 50 ± 40 = 90, 10.
Place the object at the distant focus (object distance = 90) and the image at the closer
focus (image distance = 10). Since you are using the “right hand side” of the ellipse,
the vertex radius will be negative (its center of curvature is to the left of the surface).
Since the light reflects, the image distance is negative also.
1. Choose the File > New menu to launch the New Lens Wizard, and click Next to
bypass the welcome screen.
2. Click the Blank Lens button and click Next.
3. On the pupil screen, accept the default for now (EPD 2 – we will later change
this to object numerical aperture, but this is not available now because the
default object distance is infinite). Click Next.
4. Click Next on the next four screens, accepting the default wavelength and
object angle (zero), and click Done on the final screen.
5. In the LDM spreadsheet window, change the object thickness to 90.0, the
Y radius of surface 1 (stop) to –18.0, the thickness of surface 1 to –10, and the
refract mode for s1 to Reflect (double-click the word Refract).

6. Choose the Lens > System Data menu to display the System Data window. On
the Pupil page, change the pupil specification to Object Numerical Aperture,
and the value to 0.4, then click the Commit Changes button.
7. Go to the System Settings page in the System Data window and change the title
to something like Ellipse.
8. Choose the Display > View Lens menu and on the Plot Parameters tab,
change the start surface in the Surface Span spreadsheet to Object, then click
the Ray Definition tab.

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9. Click in the first cell of the Fan of Rays spreadsheet to get the default ray fan,
then click OK.
Search
The following View Lens output window is displayed.

What’s wrong with the picture? Only some of the inner zone rays are drawn.
The default spherical reflector can’t trace the marginal rays for NAO 0.4—you
need to make the surface a conic. Leave the View window open so you can
rerun it in a moment.
10. In the LDM spreadsheet, right-click on the surface type for surface 1 (stop) and
choose Surface Properties from the shortcut menu.
11. On the Surface Type page in the Surface Properties window, choose Conic
from the dropdown list labeled Type, then click another cell to commit this
change.
12. Change the value for the parameter Conic Constant (K) to –0.64 and tab or
click elsewhere to commit this change.

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Search

13. Click the Execute button in the View Lens window.

Now the picture is what you might expect. All of the rays from the left focus
(object point) are perfectly focused to the right (close to vertex) focus. Note that
this perfect image will degrade pretty quickly if you move the object point off
the axis. Try changing the object height to 1 mm and see what happens to a
quick spot diagram or ray aberration plot.

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Polynomial Aspheres
Search
The polynomial asphere is a rotationally symmetric surface whose surface profile
(sag) is given by the following equation.

cr 2 - + Ar 4 + Br 6 + Cr 8 + Dr 10 + Er 12 + Fr 14 + Gr 16 + Hr 18 + Jr 20
z = -------------------------------------------------
1 + 1 – ( 1 + k )c r 2 2

where:
z(r) 2 2
r is the radial distance = x + y
c is the curvature at the pole of the
r surface.
k is the conic constant.
z A through J are the 4th through 20th
order deformation terms.

It is a 20th-order deformation to a base conic (starting at the 4th order; the 2nd
order term is essentially equivalent to the curvature). If the aspheric coefficients
A-J are all zero, the surface reduces to a pure conic. If the conic constant k=0, the
surface is a 20th order deformation to a sphere.
Since the equation of a parabola is a pure 2nd order equation, if the conic constant
for a polynomial asphere is -1, the equation is an exact 20th order polynomial
(technically, spheres and general conics are of infinite order).

Fresnel Surface
The ASP type surface can also be used to represent a Fresnel surface (with
infinitesimally narrow zones). Such a Fresnel surface is specified by making the
Fresnel base curvature (CUF) non-zero (for a flat substrate, use a very small
curvature, such as 0.000001). The surface sag then follows the base substrate, but
the surface slope is defined by the derivative of the equation above.
In the list of surface types, you will find this listed as the type Thin Fresnel. This
entry really creates an ASP type surface with access to the Fresnel base curvature.
You will also find other types of Fresnel surfaces in list of surface types. The type

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Fresnel Planar Substrate (SPS FRS) is the finite-facet-size version of the basic
(ASP-based) Fresnel. Search in the CODE V Reference Manual for SPS FRS or
Search
Fresnel planar to find more information on these surfaces.

Entering an Asphere
This procedure applies to every type of non-spherical surface.
1. In the LDM spreadsheet window, right-click on the Surface Type cell of the
surface you wish to change and choose Surface Properties from the shortcut
menu. This brings up the correct page of the Surface Properties window.
2. Choose Asphere in the Type field, and click in another field to commit this
change (the correct coefficients for this type will now appear).
3. Enter the appropriate special surface data (if known) in the labeled data fields.
Most often you will not know a value but will use optimization to vary it.
4. To make a parameter variable (such as the conic constant or an aspheric
coefficient), right-click on the parameter and choose Vary from the shortcut
menu.

Tip: Aspheric “sag” is the deviation from a sphere caused by the aspheric
deformation. To display tables of sag-related data for any non-spherical surfaces
in the lens, choose the Analysis > Fabrication Support > Fabrication Data
Tables menu and click the Sag Data tab. Select the Display sag table checkbox
and any special options.

It’s a good idea to check with the fabricators before designing a system with
aspheres or other non-spherical surface profiles. Molding, diamond turning, and
other methods have limitations in achievable sag, element size, aperture shape,
part thickness, materials, etc. You can constrain these things in CODE V
optimization if you are aware of the requirements.

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Aspheric Singlet Example

Search
For this example, you will enter and optimize a plano-convex 50 mm diameter f/2
singlet. The front radius is 52 mm, the thickness is 10 mm, and the material is BK7.
The back surface is plano. You will do this monochromatically at 587.56 nm
(d light). You will only worry about the on-axis field (not a good idea, in general,
but OK for this example). Finally, you will insert a paraxial image solve to set the
image distance. Here are the steps:
1. Choose the File > New menu to launch the New Lens Wizard, and click Next
on the welcome screen.
2. Choose CODE V Sample Lens and click Next, then scroll to locate the lens
cv_lens:singlet.len in the list and click on it. Click Next.
3. On the Pupil screen, change the Pupil Specification to Image F/Number,
enter 2.0 for the value, and click Next. A dialog box displays to tell you that
solves in the lens will be deleted if you choose f/number; click Yes to close this
dialog box, since we won't need the solves.
4. On the New Lens Wizard’s Wavelengths screen, double-click the supplied
value (500 nm) and choose the d wavelength (587.56 nm) from the list, then
click Next.
5. The reference wavelength and field data (axis only) are OK; click Next on each
screen (Done on the final screen), or just click Finish on the Wavelength
screen. This completes the New Lens Wizard and the lens is defined.
6. In the LDM spreadsheet window, change the Y radius of s1(stop) to 52.0, the
thickness of s1 to 10.0, and the Y radius of s2 to 0.0 (this is a shortcut for
entering a zero curvature or flat surface, since a zero radius is impossible—it
will display as Infinity).
7. Right-click on each radius and choose Freeze from the shortcut menu (the only
variable you need here is the image surface defocus, the thickness of the image
surface). The LDM spreadsheet should look like this:

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Now you can analyze this lens as a starting point. Use the Quick Lens Drawing
and Quick Ray Aberration Plot buttons on the toolbar, shown in the following
Search
illustrations.

The spherical aberration is quite large. Note the 2 mm scale on the ray aberra-
tion plot.
Now you can make the front surface aspheric, and allow the fourth and sixth
order coefficients to be variables for optimization.
8. In the LDM spreadsheet window, right-click the Surface Type for surface 1
(stop) and choose Surface Properties from the shortcut menu.

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9. In the dropdown Type list, choose Asphere, then click in another cell.
Search 10. To make the coefficients variable, right-click in the 4th Order Coefficient field
and choose Vary Parameter (leave the value at the default, 0.0). Do the same
with the 6th Order Coefficient field.

11. Choose the Optimization > Automatic Design menu. Since you are only
varying aspherics and defocus, the gross properties of the lens such as focal
length cannot change, and you won't need any specific constraints. Click OK to
start this default AUTO run. Look at the Surface Properties window again.

12. Use the Quick toolbar buttons again to make a new lens picture and ray
aberration curve and compare them to the starting versions. Note that the
automatic scale factor on the Quick Ray Aberration Plot is now 0.0045 mm
(was 2 mm), and the curve has multiple crossing points and residual higher
order aberration.

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Search

If you return to the Surface Properties window and make the 8th-order coefficient
variable, then re-run the optimization window (Optimization > Automatic Design
> OK) and aberration curve, the scale factor will be 0.0005 mm and the lens will be
essentially perfect (on-axis only, one wavelength only, SA corrected to 8th order).

13. Choose the File > Save Lens As menu to save your optimized aspheric singlet
in a file for possible later use.

Tip: When optimizing an asphere, you should vary either the 4th-order
coefficient (A) or the conic constant (K), but not both. They are often roughly
equivalent in optical effect, but if the vertex curvature of the surface is very weak
(as in the Schmidt corrector), the conic will not be an effective variable, and you
should use the 4th-order term.

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Diffractive Surfaces
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What Are Diffractive Optics?

In addition to conventional diffraction gratings, other types of diffractive optical
elements (DOEs) have come into widespread use in recent years. These range from
holographic head-up displays (HHUDs) for aircraft, to binary optics, to diamond-
turned diffractive correctors on IR lenses. CODE V allows you to apply diffractive
properties to any surface type except lens modules (MOD). The types of diffractive
properties you can define on a surface include:
• Linear grating parameters
• DOE properties (kinoform/binary)
• Volume holographic optical element (HOE) parameters

Color-Corrected IR Lens

The example shown above is a two-element f/1 thermal infrared objective. A

diamond-turned DOE on surface 2 allows diffraction-limited performance over the
8-12μm band (8,000 - 12,000 nm) with only two germanium elements (a
conventional design requires a third non-Ge element for similar performance).
There is also a conventional asphere on surface 1.

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To open this predefined lens:

Search 1. Choose the File > New menu to launch the New Lens Wizard. Click Next twice.
You will be on the page in the New Lens Wizard where the CODE V sample
lens database is listed.
2. Scroll to locate the lens file cv_lens:bindoub.len and click on it.
3. Click the Finish button to read the lens into CODE V (if you prefer, you can
click Next on the remaining New Lens Wizard screens to see the system data
values used in this lens model).
4. Click the Quick 2D Plot button or another lens drawing feature (e.g.,
QuickView macro, shown above) to see a picture of this lens.
The LDM spreadsheet for this lens is shown below. Note that there is a small
“diffract” symbol in the Refract Mode column for surface 2 (this indicates that
although the surface is transmissive and nominally refractive, ray direction is
affected also by the diffractive properties).

Diffractive surfaces have a number of special features and therefore they have their
own page in the Surface Properties window. If you right-click on the surface type
for s2 (Sphere) and choose Surface Properties, you will find only the Y Radius
listed in the Surface Properties window. Click the Diffractive Properties item in
the navigation tree on the left side of the window and you will see the following
page:

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Search

In this case, construction points have been specified as if the surface were actually
holographic, although the two points are located at the same coordinates and thus
contribute no power to the diffractive. You could change the Diffractive Surface
Type to Phase Polynomial (Kinoform/Binary) and it will have no effect in this case
(this actually zeroes out the construction point coordinates).
Note that the polynomial type is rotationally symmetric, and that there are phase
terms from R**2 to R**20. These phase terms can be varied in optimization, much
like aspheric coefficients (it is best to introduce lower order terms first, adding
higher orders in later optimization runs).

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Ray Grid Issues

Search
There are some numerical sampling issues to consider when optimizing and
analyzing systems with non-spherical surfaces. CODE V uses ray grids for many
calculations, including most analysis tasks as well as optimization. In the case of
analysis options (MTF, PSF, etc.), the default grids are usually dense enough to
allow them to “see” the surface variation caused by aspheres and other non-
spherical surfaces, although there can still be sampling problems related to FFT and
other calculations (these issues are discussed in the CODE V Reference Manual in
options such as PSF, CEF, and BPR).
In optimization, smaller grids are typically used because of the iterative nature of
the calculations (the error function must be evaluated many times). The value that
determines the ray grid is called DEL. In the Automatic Design dialog box, the field
is Ray interval (in pupil fraction), and it is found on the Error Function
Definitions and Controls tab in the Ray Grid Controls area. The program uses a
default of 0.385 for all-spherical systems (12 rays in the half pupil), and if there are
non-spherical surfaces, it changes to 0.22 (34 rays in half pupil). Note that the
specified number of rays is traced for each wavelength, field, and zoom position.
This is an important issue with aspheres, because high order polynomials have the
ability to change the surface slope very rapidly. If there are too few rays, AUTO
will not see some portions of the surface that can cause large ray deflections. It may
calculate an error function that does not represent the real performance.
To see the effect of different ray grid sizes in AUTO, you can run the supplied
macro AUTOGRID.SEQ. Choose the Tools > Macro Manager menu, locate the
macro under Sample Macros/Optimization, and click Run. Enter the DEL value
0.22 as shown and click OK.

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The output is a plot showing the ray distribution. The plot will give you an idea of
how many rays the program will use, as well as their positions. Smaller values
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(denser grids) mean more rays. If you use high order aspheres or diffractives, you
should consider using a smaller DEL (e.g., 0.15 which gives 70 rays), and also run
the AUTOGRID macro to visualize the grid that AUTO will use.

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182 CODE V Introductory User’s Guide