2013-07-01
Prof. Herbert Gross
Friedrich Schiller University Jena
Institute of Applied Physics
Albert-Einstein-Str 15
07745 Jena
Solution of Exercises
Lecture Optical design with Zemax for PhD – Part 10
10.1
Field lens flattener
A field lens near to the image plane can help to correct a system for field curvature.
a) Load the f = 50 mm lens AC 300-050-C of the Thorlabs lens catalog. let the incoming light be a
collimated beam at  = 0.55 m with a diameter of 10 mm. Define the three field points for initail field
angles of 0, 3 and 5 degree.
b) Calculate the Seidel bar diagram and the spot diagram. What are the dominant aberrations of the
system ?
c) Introduce a concave-plane field lens with thickness 5 mm. What is the preferred material and what
is the best focal length to correct the system for Petzval curvature ? The distance between the
achromate and the field lens should be optimized only on axis.
d) What is the result, if the spot is optimized for all field points ?
Solution:
The achromate with f = 50 mm looks like the following figure:
b) The Seidel diagram and the spot diagramm looks as follows. The dominant aberratins are
astigmatism and field curvature. Spherical aberration and coma are only a little bit smaller.
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c) The additional field lens is inserted and the distance between the achromate, the front surface
radius and the refractive index are chosen be be variable. In the merit function, the spot only for the
axis point and the field curvature (FCUR) are forced to be corrected. The first result gives a model
index of n = 1.84. The glass, which is nearest to this value if N-LASF41 with n = 1.83913. After
inserting this, the system is re-optimized and becomes free of field curvature:
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d) If the spot is optimized for all field points, the mean curvature is reduced, the astigmatism is nearly
symmetrically around the image plane. The field lens looks completly different, the astigmatism is
reduced.
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10.2 Apochromate
An apochromatic lens shows a common image location for at least three wavelengths.
a) Load the achromate LAO-100.0-30.0 from the CVI Melles Griot catalog. Define an entrance pupil
diameter of 25 mm and the color sequence e-F'-C'. The variation of the intersection length with the
wavelength can be seen in the diagram, which is obtained in the menue ANALYSIS /
MISCELLANEOUS / CHROMATICAL FOCAL SHIFT.
b) Add a third thin cemented lens with the material BK7. Establish a chromatical focal shift, which is
identical for the three chosen wavelengths. The numerical aperture of the system should be
maintained. Can the apochromatic correction be obtained ?
c) Now choose different glass combinations to achieve an apochromatic correction. In particular the
materials with anormal partial dispersions like FK54 or KZFSN4 should be checked.
Solution:
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a) System data and chromatical focal shift:
b) The lens is added, the merit function is defined with the default for spherical correction, the Fnumber of 4 and the axial aberration AXCL for the wavelengths 1-2 and 2-3.
It is seen, that the three vanishing focal shifts can not be achived.
c) If different glasses are used, especially KZFSN4 is incorporated, a common image location for
three wavelengths can be obtained.
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10.3
New Achromate and wide field system
A new achromate is a cemented component, that is optimized for large field applications. In this case,
the Petzval condition is the basis for the refractive power distribution and the achromatization is no
longer a correction goal. In this case, a large difference in the refractive indices is more important than
a large spreading of the Abbe number.
a) Establish a classical achromate made of BK7 and SF6 with focal length f = 100 mm and an object
at infinity from the scratch. Insert a stop 20 mm before the lens and select the wavelength 546.07 nm
and an entrance pupil diameter of 4 mm. The system should be used on axis andfor a maximum field
angle of 20°. Optimize the radii for the default merit function and evaluate the system performance.
b) Extend the system to a finite imaging system with magnification m = -1 by doubling the system.
The first group of lenses should by reversed and the stop is in the middle of the system to get a
complete symmetric layout. What is the dominating aberration. Insert a second field point in the zone
of the field at 14°.
c) Now the second part of the symmetric system is scaled down by a factor of 2. This delivers a
system with a magnification of m= -0.5. Therefore we no longer have a symmetric layout. What
happens with the system quality ?
d) To improve the system add two meniscus lenses made of SK12 near to the cemented components
towards the stop with the exact 1:2 scaling. Optimize the radii to improve the system while preserving
the mirror-symmetry. Can the astigmatism be removed ?
e) Now optimize the radii without any anti-symmetric constraints. Show, that the performance can be
improved significantly. Finally enlarge the numerical aperture of the system to a value, that is just
below the diffraction limit. To have some more degrees of freedom, the distances around the
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meniscus lenses are also set as variable. To guarantee a useful solution, the magnification (PMAG 0.5) and the overall length of the system (TOTR 190.5) must be forced in the merit function to be
constant. Show, that the field curvature is corrected by the mensicus shaped lenses to a very good
flattened field.
Solution:
a) The approach delivers the follwing system:
The performance is nearly diffraction limited, a residual astigmatism is seen for the field point.
b) the extension of the systems gives the following layout.
The astigmatism is enlarged in the field, this is seen at the line-shaped focus at 20° field.
c)
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The scaling can not be performed by a simple single command in Zemax. Therefore for the values of
the distances and thicknesses are set by hand to half the values, the radii are calculated by setting a
pick up of the corresponding surface with a scaling factor of -2 (not -0.5 !).
It is seen, that the astigmatism for the outer field is still the limiting aberration.
d) The system now looks as follows:
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It is seen, that the performance is much better, there is nearly no longer astigmatism inside.
e) A complete arbitrary optimization of the radii gives the following result:
In the second step, the entrance pupil diameter is enlarged to a value of 7 mm. In the merit function
the two requirements are added:
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The rms-plot against the focus shows nearly coincident image locations over the field. This means,
that the field curvature is well corrected.