ECEN 4616/5616
4/8/2013
Design of a 10x, 0.25 N.A., Microscope Objective
We intend to construct the objective from two separated achromatic doublets.
Researching the literature shows that such objectives are essentially limited to N.A.s of
0.25 or less. Higher N.A. can be achieved, but with significant complication to the
optical design. The following table from a microscope informational website
(http://micro.magnet.fsu.edu/primer/anatomy/numaperture.html ) confirms that this
design form is limited to ≤ 0.25 N.A.:
Objective Numerical Apertures
Magnification
Plan
Achromat
(NA)
Plan
Fluorite
(NA)
Plan
Apochromat
(NA)
0.5x
0.025
n/a
n/a
1x
0.04
n/a
n/a
2x
0.06
n/a
0.10
4x
0.10
0.13
0.20
10x
0.25
0.30
0.45
20x
0.40
0.50
0.75
40x
0.65
0.75
0.95
40x (oil)
n/a
1.30
1.00
60x
0.75
0.85
0.95
60x (oil)
n/a
n/a
1.40
100x (oil)
1.25
1.30
1.40
150x
n/a
n/a
0.90
“Standard” Microscope Layout:
Eyepiece
“Artistic”
Ray Trace
Objective
pg. 1
ECEN 4616/5616
4/8/2013
The “standards” for microscope design have historically varied widely.
(For a brief description of this history, you can find websites like this one:
http://www.microscopy-uk.org.uk/mag/indexmag.html?http://www.microscopyuk.org.uk/mag/artapr10/rp-compat.html)
During the last half of the 20th century, however, a (sort-of) standard mechanical
layout was as follows:
 Tube length: 160 mm
 Tube diameter (inner): 23 mm. (Since the eyepieces slip into the tube, the
maximum clear aperture of the eyepiece optics is considerably less than
this.)
 Bottom of tube to focal plane: 36mm (Japanese) or 45mm (German).
(This is only of importance when you have multiple objectives mounted on
a turret below the tube – they should all be the same standard!)
Specifications:

10X: The objective is to produce a real image of the specimen that is magnified
10 times at a distance of 160 mm (standard microscope tube length) behind the
mounting shoulder of the objective:
160 mm
Objective
10X Image
Eyepiece
Specimen
pg. 2
ECEN 4616/5616

4/8/2013
0.25 NA: The sine of the half-angle of the light cone from the specimen to the
objective is to be 0.25 (14.48 degree half angle cone).
aA ==30
dego
14.48
a
Since the resolution on the specimen is of prime importance, we will design the objective
backwards from the way it is to be used – rays will be traced from the image to the
specimen. This way, the PSF and MTF analysis by the ray trace program will directly
indicate the resolution achieved at the specimen. We can think of this as “imaging the
detector onto the specimen”.
Initial Paraxial Layout:
h
u
l
u’
l’
K
We are given that l  160mm , 𝑢′ = 0.26, and M  
1
.
10
Using the paraxial equations, we can calculate that:

𝑀=

1



𝑙′
𝑙′
1
𝑙
⇒ 𝑙 ′ = 16𝑚𝑚
1
= 𝑙 + 𝑓 ⇒ 𝑓 = 14.545𝑚𝑚
ℎ
𝑢′ = − 𝑙′ ⇒ ℎ = 4.16𝑚𝑚
𝑢
𝑀 = 𝑢′ ⇒ 𝑢 = 0.026 (tan 1.49𝑜 )
and
𝑓
𝑓
𝐹# ≡ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 2ℎ = 1.7
pg. 3
ECEN 4616/5616
4/8/2013
Note that the F/# is faster than the practical limit for achromats (~ F/2 -- determined by
scanning the various lens catalogs in Zemax). This confirms our decision to divide the
design into two achromats.
Note on resolution:
The maximum resolution of the objective (period of cutoff spatial frequency) will be 𝑝 =
𝜆
≅ 1µ𝑚 for green light (0.5µm wavelength). Hence, the spotsize in the 10X
2𝑁.𝐴.
magnified image will be 10µm. This is matched well for direct detection using a digital
detector with no more than 10µm sized pixels.
The maximum resolution of the “standard” human eye is 1 arc min (0.0003 rad). At the
standard near-vision distance of 250 mm, this corresponds to a spot size of 0.003*250 =
.075mm, or 75 microns. A 10x eyepiece will then reduce the just-resolvable spot size to
7.5 microns, slightly less than the smallest resolvable spot in the objective’s image. A
slight excess of “empty resolution” is desirable, as it prevents the user from straining at
the limit of their eye’s resolution.
Thus, a 0.25N.A., 10X microscope objective is well matched directly to a reasonable
digital detector, and to the Human eye using a 10X eyepiece.
Revised Paraxial Layout:
u2
h1
u1
l
h2
d1
K1
K2
u3
d2
For now, we arbitrarily set d2 = 10mm. This may not be optimum, but the optimizer can
change it later, while maintaining an adequate working distance. We also divide the ray’s
angle change equally between the two lenses.
We now calculate the additional variables. Note that u1, l, h1, and u3 are still the same.
u1
tan(1.490)=0.026
u2
u2 = tan(3-1)/2 = tan(-80)= -0.14
u3
-0.26 = tan(-14.60)
h1
h1 = -u1l = 4.16 mm
h2
h2 = -u3d2 = 2.6 mm
l
-160 mm
d
d1 = (h2-h1)/u2 = 11.14mm
K1
K1=(u1-u2)/h1 = (25.06 mm)-1
K2
K2=(u2-u3)/h2 = (21.67 mm)-1
pg. 4
ECEN 4616/5616
4/8/2013
Zemax Reality Check:
(2x vertical stretch)
Layout
4/8/2013
Total Axial Length: 181.14000 mm
Vertical scale stretched by 2.0000 X
10XMicro_paraxial.zmx
Configuration 1 of 1
Calculate Achromat Starting Designs:
We now need to replace the paraxial lenses with achromats. Pick some likely glass
combination that has a fairly large difference in V-numbers. It is good to stay away from
“exotic” glasses at first, as they can greatly increase the fabrication cost. A good guide
for achromat glasses is Edmund Optics inexpensive achromats, accessable from the Lens
Catalog dialog box (click on the “Len” tab on the menu bar).
pg. 5
ECEN 4616/5616
4/8/2013
An easy way to see what these lenses are made of is to insert a bunch of dummy surfaces
at the top of the Lens Data Editor, then select a lens and hit “Insert”:
pg. 6
ECEN 4616/5616
4/8/2013
Highlighting a glass in the LDE, then clicking on the Glass Catalog button (“Gla”) will
bring up the data on that glass:
Since our lenses are still fairly fast, we would like two glasses with fairly high indices
and a large difference in V-numbers. After looking at a number of achromats and
glasses, we pick:
Glass #
1) LAK21
2) SFL6
Index
1.640495
1.805182
Vd
60.1019
25.3939
Recall that the paraxial formulas for an achromatic doublet are:
K1  K2  K and
VK
VK
K1  1
and K 2   2
V1  V2
V1  V2
Putting the glass and paraxial power values into these formulas (glass 1 = LAK21, glass 2
= SFL6), we get:
K1=1.731644 K, and K2 = -0.731644 K
pg. 7
ECEN 4616/5616
4/8/2013
Using the thin lens formula, K  (n  1)(c1  c2 ) , and assuming, for a starting point, that
the positive lens of the doublet is equiconvex (c2= -c1), we get the starting point lens
parameters:
Paraxial
lens
1
2
f
f1
R1=-R2
f2
R2
25.9 mm
21.87 mm
14.956885 mm
12.6296 mm
24.086 mm
16.178mm
-35.34 mm
-29.89 mm
-156.8665 mm
-104.4089
(Where we have used K=1/f, c = 1/R to make the values easier to enter into Zemax.)
Zemax Optimization:
Entering the first achromat into Zemax, and re-focusing the system:
pg. 8
ECEN 4616/5616
4/8/2013
The lens is acting as an achromat:
But, the performance is not great:
TS Diff. Limit
TS 0.0000 mm
TS 6.0000 mm
1.0
0.9
Modulus of the OTF
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
100
200
300
400
500
600
700
800
900
1000
Spatial Frequency in cycles per mm
Polychromatic Diffraction MTF
4/8/2013
Data for 0.4861 to 0.6563 µm.
Surface: Image
10XMicro_L1_P2.ZMX
Configuration 1 of 1
pg. 9
ECEN 4616/5616
4/8/2013
There is a large amount of Spherical Aberration Present:
STO
Spherical
2
Coma
3
Astigmatism
4
Field Curvature
5
Distortion
Axial Color
SUM
Lateral Color
Seidel Diagram
4/8/2013
Wavelength: 0.5876 µm.
Maximum aberration scale is 0.05000 Millimeters.
Grid lines are spaced 0.00500 Millimeters.
10XMicro_L1_P2.ZMX
Configuration 1 of 1
A merit function was constructed to hold the 3rd order spherical and chromatic focal shift
to low values – this mimics the old technique of designing by making small changes
while keeping 3rd order aberrations low. It helps keep simple systems from assuming
weird proportions (as long as the degrees of freedom are available to limit the
aberrations):
Both wavefront and spot size default functions were tested – the wavefront worked better.
pg. 10
ECEN 4616/5616
4/8/2013
The optimization results were good:
TS Diff. Limit
TS 0.0000 mm
TS 6.0000 mm
1.0
0.9
Modulus of the OTF
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
100
200
300
400
500
600
700
800
1000
900
Spatial Frequency in cycles per mm
Polychromatic Diffraction MTF
4/8/2013
Data for 0.4861 to 0.6563 µm.
Surface: Image
10XMicro_L1_P2_Opt.ZMX
Configuration 1 of 1
STO
Spherical
2
Coma
3
Astigmatism
4
Field Curvature
5
Distortion
Axial Color
SUM
Lateral Color
Seidel Diagram
4/8/2013
Wavelength: 0.5876 µm.
Maximum aberration scale is 0.02000 Millimeters.
Grid lines are spaced 0.00200 Millimeters.
10XMicro_L1_P2_Opt.ZMX
Configuration 1 of 1
(Note the scale on the Seidels is 40% of the unoptimized scale.)
pg. 11
ECEN 4616/5616
4/8/2013
Layout
4/8/2013
Total Axial Length:
35.31380 mm
10XMicro_L1_P2_Opt.ZMX
Configuration 1 of 1
Continuing on and replacing the second paraxial lens:
Layout
4/8/2013
Total Axial Length:
38.53689 mm
10XMicro_L1opt_L2_nopt.ZMX
Configuration 1 of 1
Re-optimizingThe lens was re-optimized, after adjusting the merit function to include the
second lens.
At first, just the second lens was optimized, but this didn’t produce satisfactory results, so
both were optimized together:
pg. 12
ECEN 4616/5616
4/8/2013
Results, however, were still disappointing:
TS Diff. Limit
TS 0.0000 mm
TS 6.0000 mm
1.0
0.9
Modulus of the OTF
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
100
200
300
400
500
600
700
800
900
1000
Spatial Frequency in cycles per mm
Polychromatic Diffraction MTF
4/8/2013
Data for 0.4861 to 0.6563 µm.
Surface: Image
10XMicro_L1opt_L2_opt.ZMX
Configuration 1 of 1
The layout diagram showed that the first lens had changed a lot, but the second had not.
Possibly, it was a mistake to optimize the first lens in the presence of the second paraxial
lens – both lenses, perhaps, should have been optimized together:
Layout
4/8/2013
Total Axial Length:
42.54483 mm
10XMicro_L1opt_L2_opt.ZMX
Configuration 1 of 1
pg. 13
ECEN 4616/5616
4/8/2013
The obvious next thing to try would have to been to back up, put both starting lenses into
the design, then optimize that.
However, it was late and I wanted to go to bed, so I decided to turn the “Hammer”
optimization algorithm loose on the system to see if it could recover by itself.
After about 30 minutes, with only moderate results (to be sure, I should have left it going
all night), I decided to allow the Hammer algorithm to substitute other Schott glasses, in
case the ones I had selected were somehow limiting the results (instead of my optimizing
order!). This is done by right-clicking on the glass name in the Lens Design Editor and
filling in the following dialog box:
Often, it would be wise to limit the glass selection to less than a full catalog (which
contains obsolete glasses). This can be done easily by following the directions in the
manual on creating new glass catalogs. Make a copy of the Schott catalog, for example,
re-name it – say “Schott_Preferred” – and delete all the obsolete glasses. You can also
create a catalog to match the glass inventory of a manufacturer.
Overnight run of “Hammer” with glass substitution resulted in a good system:
pg. 14
ECEN 4616/5616
4/8/2013
pg. 15
ECEN 4616/5616
4/8/2013
The glasses had all been changed – it was evident that the system was not achromatic per
lens (see the Seidel Diagram), but was dividing the aberration corrections between the
lenses.
While this resulted in a good system (better than the one in Zebase!), the division of
aberration correction will interfere with any attempts to convert this lens to use of stock
achromats. It would be better to do the optimization with additional operands in the MFE
that constrained each lens to be individually corrected.
pg. 16
ECEN 4616/5616
4/8/2013
Previous attempt at Off-The-Shelf (OTS) microscope lens:
Doing this is tedious, as there are no “Substitute” solves that can try different
catalog lenses in Zemax – it all has to be done manually.
Starting from a similar design, catalog lenses were substituted for the optimized
lenses, and the system re-optimized (except for the catalog lenses, of course!).
This process only produced reasonable results after the N.A. was reduced to
0.18, and a third lens was added:
Layout
Stock lens 10x microscope objective, 0.125 NA
4/8/2013
30.39202 mm
Total Axial Length:
MDE_04_OTS.zmx
Configuration 1 of 1
Within those constraints, however, the results were fairly good:
pg. 17
ECEN 4616/5616
4/8/2013
TS Diff. Limit
TS 0.0000 mm
TS 5.0000 mm
1.0
0.9
Modulus of the OTF
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
74
148
222
296
370
444
518
592
666
740
Spatial Frequency in cycles per mm
Polychromatic Diffraction MTF
Stock lens 10x microscope objective, 0.125 NA
4/8/2013
Data for 0.4861 to 0.6563 µm.
Surface: Image
MDE_04_OTS.zmx
Configuration 1 of 1
0.4861
0.5876
0.6563
OBJ: 5.0000 mm
IMA: 0.000 mm
IMA: -0.508 mm
40.00
OBJ: 0.0000 mm
Surface: IMA
Spot Diagram
Stock lens 10x microscope objective, 0.125 NA
4/8/2013 Units are µm.
Field
:
1
2
RMS radius :
2.132
4.439
GEO radius :
4.090
12.831
Scale bar : 40
Reference : Chief Ray
MDE_04_OTS.zmx
Configuration 1 of 1
pg. 18
ECEN 4616/5616
1
Spherical
4/8/2013
2
3
Coma
4
5
6
Astigmatism
7
Field Curvature
8
STO
Distortion
10
Axial Color
11
SUM
Lateral Color
Seidel Diagram
Stock lens 10x microscope objective, 0.125 NA
4/8/2013
Wavelength: 0.5876 µm.
Maximum aberration scale is 0.01000 Millimeters.
Grid lines are spaced 0.00100 Millimeters.
MDE_04_OTS.zmx
Configuration 1 of 1
pg. 19