ECEN 4616/5616
Optoelectronic Design
Class website with past lectures, various files, and assignments:
http://ecee.colorado.edu/ecen4616/Spring2014/
(The first assignment will be posted here on 1/22)
To view video recordings of past lectures, go to:
http://cuengineeringonline.colorado.edu
and select “course login” from the upper right corner of the page.
Lecture #22: 3/05/14
Designing a 10X Microscope Objective
First, what does a ’10x’ objective mean?
“Standard” Microscope Layout:
Eyepiece
Tube
Objective
Condenser
The basic microscope consists of an
objective lens at one end of a tube and an
eyepiece at the other. The ’10x’ refers to
the fact that the objective projects a real
image just in front of the eyepiece that is
10 times as large as the object.
Eyepieces are also rated according to their
magnification power (according to the
formula we previously derived: M =
250mm/f).
So, a 10x objective combined with a 10x
eyepiece would produce an apparent
magnification of 100x.
The ‘Condenser’ in the simple microscope shown is a concave mirror which
focuses an external light source onto the object slide.
More sophisticated instruments might have a powered light source.
Designing a 10X Microscope Objective
Knowing that the objective is to produce a 10x size real image helps, but doesn’t
determine the actual dimensions involved, such as object and image distances, etc.
Looking up ‘microscopes’ in the EdmundOptics catalog website allows us to find a
description of the standard microscope dimensions. There are two:
The German (DIN) standard.
The Japanese (JIS) standard.
We will arbitrarily choose the DIN standard: Hence there is 205 mm
between the object and 10x magnified image.
Designing a 10X Microscope Objective
Well, we still don’t know what focal length lens we need, but we have enough
information to do a paraxial layout:
u’
u
l
l’
l
 10
l
Hence:  l  17.727, l   177.272
We also know that:
l   l  195 &
And from the imaging equation:
1 1 1
 
l f l
We can calculate the focal length: f  16.116mm
Designing a 10X Microscope Objective
We need another piece of information, the Numerical Aperture (NA) of
the objective. In general, microscope objectives are designed to as high
a NA as feasible, since the ultimate resolution is dependent on the NA:

1
x 
, where
is the cutoff spatial frequency of the objective.
2NA
x
Again, we look at commercially available microscope objectives at
Edmund Optics, and see that all 10x standard objectives have NA=0.25
10X DIN Achromatic Intl
Standard Objective
#36-132
Type
Achromatic
Magnification
10X
Effective Focal Length EFL
(mm)
16.60
Field of View, 18 Diameter
Field Eyepiece (mm)
1.80
Working Distance (mm)
6.30
Numerical Aperture NA
0.25
We also note that:
• Typical FOV = 1.8mm
• Working Distance = 6.3mm
(Working distance is the distance from the object to the first lens.)
Designing a 10X Microscope Objective
h
u’
u
l
l’
Going back to our paraxial layout, we can now calculate the lens (or
entrance pupil) diameter. Remember that the Gaussian ‘angle variable’, u,
is actually the tangent of the angle, so:
  sin1  0.25  , u  tan( )  u  tan  sin1  0.25    0.258
h
 h  (0.258)( 17.727)  4.573mm
l
f
The F/# of the lens, therefore is: F # 
 1.76
2h
u
The question then presents itself: Can we make a reasonable 10X,
0.25NA objective from a single achromat?
Designing a 10X Microscope Objective
To find out if a single achromat would make an OK 10X, 0.25NA objective, we can
look at a lens catalog in Zemax for achromats that have focal length of ~16mm and
diameter of at least 9.2mm (2h):
We pick a likely candidate with similar specifications and test it stopped
down to 0.25NA:
Designing a 10X Microscope Objective
The layout window doesn’t look
bad, but:
Chromatic focal shift is
twice the diffraction
limited range, and:
The MTF barely gets to 100 cycles/mm,
whereas the diffraction limit (2NA/λ)
should be nearly 900 cycles/mm.
So, unless we can design a far, far better
achromat than Edmund Optics (unlikely), it
looks like a single doublet won’t work.
Designing a 10X Microscope Objective
Revised Paraxial Layout – Two Lenses
u1
K1
u0
d0
K2
h2
h1
d1
u2
d2
For now, we arbitrarily set d0 = 10mm, d1 = 15mm (and hence, d2=170mm). This may
not be optimum, but the optimizer can change it later, while maintaining an adequate
working distance. Calculating the new parameters:
u
u0  tan  sin1  0.25    0.258, u2 =- 0 =-0.0258 (both unchanged)
10
h
h
u0  1 ,  h1  2.58 mm, u2  2 ,  h2  4.386 mm
d0
d2
u1 
K1 
u1 is not far from the average of u0, u2 (0.116), so the job of refracting
h2  h1
 0.1204 the marginal ray is fairly evenly divided between the lenses.
d1
u1  u0
u  u1
 0.0533, K 2  2
 0.0333
h1
h2
 f1  18.75mm, f2  30mm
And the F/#s are 3.6 and 3.42
Designing a 10X Microscope Objective
Revised Paraxial Layout
f2
f1
d0
d1
l’
Just listing the values that go into Zemax:
• d0 = 10 mm
• f1 = 18.75 mm (dia=5.16, F#=3.6)
The F#s are now
• d1 = 15 mm
reasonable for achromats
• f2 = 30 mm (dia=8.8, F#=3.4)
• l’ = 170 mm
Zemax Reality Check
Designing a 10X Microscope Objective
Picking Glasses
I searched in the Edmund
catalog for achromats near
the focal length of interest.
Several of them were
inserted into test files and
evaluated.
The best one found was
catalog # 32313:
Designing a 10X Microscope Objective
Picking Glasses
Designing a 10X Microscope Objective
Zemax Starting Solution
Highlighting the glass in the LDE and clicking on the “Len” tab gives us the
glass parameters:
N-SSK8:
Nd = 1.617728
Vd = 49.8292
N-SF10:
Nd = 1.728277
Vd = 28.5326
Designing a 10X Microscope Objective
Starting Solutions for Zemax
We will use a simple design to start the optimization: The positive achromat
element will be symmetrical. Other than adding necessary thickness, this makes
only two surface parameters per achromat:
R1
R2
-R1
The power and the surface curvatures are related by the ‘thin len
formula’:
K  (n  1)(c1  c2 )
Designing a 10X Microscope Objective
Starting Solutions for Zemax
Using the Paraxial Achromat construction equations:
K1  K 2  K , K1 
V1K
V1  V2
and
K2  
V2K
V1  V2
And the glass parameters:
N-SSK8:
Nd = 1.617728
Vd = 49.8292
N-SF10:
Nd = 1.728277
Vd = 28.5326
We get the following prescriptions: (Diameters to accommodate h1, h2 )
Achromat #1:
(f=18.75mm)
f1 = 8.0136 mm
f2 = -13.995 mm
Achromat #2:
(f = 30 mm)
f1 = 12.822 mm
f2 = -22.392 mm
R1 = 9.9004
R2 = -345.9
Diameter: 6mm
R1 =15.8407
R2 = -553.44
Diameter: 9mm
Achromat 1:
We put the calculated achromats into Zemax, in individual
files so as to check the calculations. (Are they really
achromats, and have the right focal length?)
Distance to the image
plane is found using
‘Tools-Design-Quick
Focus’.
Wavelengths are set to F,d,C:
Aperture set to 5mm diameter (~2h1 )
Analysis Windows from ‘Achromat_1.zmx’
Achromat 1:
Designing a 10X Microscope Objective
Starting Solutions for Zemax (continued)
We combine the two files, ‘Achromat_1.zmx’ and ‘Achromat_2.zmx’ by copying and
pasting the rows from the LDE into a new file: (Remember to change the object
thickness to 10 mm)
We also change the aperture type to
“Object Space NA” and set it to 0.025
Designing a 10X Microscope Objective
Starting Solutions for Zemax (continued)
Focusing and analyzing the total system reveals truly horrible results:
The Seidel Diagram gives us a clue:
Notice that the first achromat no
longer has a balanced out Spherical
Aberration.
Due to the nearness of the source,
most of the refraction is happening
at the front surface, causing that
surface’s aberrations to dominate
the sum. We need to turn the lens
around to equalize the diffraction at
the other surfaces.
Designing a 10X Microscope Objective
Reversing a Lens
We highlight the len’s
surfaces in the LDE
(remember there are
four):
And select ‘Tools-Modify-Reverse
Elements’ from the menu:
This doesn’t always work the way you
expect, so check the layout again:
It looks OK:
Designing a 10X Microscope Objective
Reversing a Lens
And the Spherical Aberration looks to be much better corrected:
Designing a 10X Microscope Objective
Zemax Starting System
A system layout, however,
shows that the total track is
far shorter than the desired
195mm (to meet the DIN
standard):
We don’t want the
optimizer to have to
make such a large change
in the system, so let’s try
some other things first.
Designing a 10X Microscope Objective
Zemax Starting System
Perhaps our assumption of a 10mm working distance is not feasible. We will let
the optimizer adjust the working distance and spacing between the achromats to
see if it can achieve the proper total track (from object to image) while maintaining
a magnification of -10:
First, we add a second field (so magnification
can be calculated) and switch the Field Type
to “Object Height” so we can precisely control
the FOV:
We put magnification and total track length in the merit function, and add the default
merit function to re-focus the system:
Note that the “Total Track” operand, TOTR, does not include the distance to the
object – hence we need to explicitly add that before weighting the sum in row 4.
Designing a 10X Microscope Objective
Zemax Starting System
It’s a good idea to put some limits on the air distances, so Zemax is not tempted to
make any of the negative (a bad habit of the Optimizer):
Designing a 10X Microscope Objective
Zemax Starting System
Finally, we make the three thicknesses variables:
• Surface 0: Working distance
• Surface 4: Achromat spacing
• Surface 8: Distance to image plane
Designing a 10X Microscope Objective
Zemax Starting System (optimized)
The optimizer doesn’t find a ‘best’ system, but a series of trade-offs, depending
on how the weights are adjusted. After some experimenting with the merit
function, this system was chosen as ‘close enough’ to start the real optimization:
Working distance: 9.6mm
Lens spacing: 5mm
Magnification: -13
The MTF is not too bad:
Designing a 10X Microscope Objective
Zemax Starting System (optimized)
The adjustments in the Merit Function weights were:
• Magnification: wt=5
• Total length: wt = 1
• Default merit function: switch to ‘spot radius’ and wt = 100
Designing a 10X Microscope Objective
(optimized)
The system is going to have a lot of
field curvature, without much ability
for Zemax to reduce it (having few
negative surfaces), so we reduce the
FOV to 0.2 mm to make it easier:
Whenever you change the field or wavelength data, you must re-create the
Default Merit Function, since those values are hard-coded into the operands
generated – so we do that, and also make all the free surfaces variable:
Designing a 10X Microscope Objective
(optimized)
After a short optimization run:
The lenses are spread out, but still
within the DIN standard range:
And the objective is diffraction limited
(for the 0.2mm FOV):
Designing a 10X Microscope Objective
(optimized)
Other choices in Optimization strategies (optimizing on larger FOV’s, or adding to the FOV
at different rates, etc.) result in fairly different systems, such as this one:
Larger working distance (15mm),
and better performance off axis
(1mm FOV)
The Problem of
Scattered Light in Fluorometers
Typical Fluorometer Optical Path
Sample
Sample Fluoresces in all
directions
Source
Source
Filter
Fluorescence
Emission Filter
Optical Stop
Collected fraction of
fluorescence light
Detector
Signal Budget for
Single-Molecule Detection Fluorometer
(Assumptions are for typical dye like Texas Red)
Light from source:
2
(One mm at sample)
Response per dye molecule:
(Peak emission @ 615nm)
1mW @ 596 nm
3 1018 photons/sec
F  Q I
≈ 100,000 photons/sec
Signal collected by receiving
optics (F/1.6, 90% efficient):
≈ 2000 photons/sec
Photon-Counting Detector:
(QE=0.4, dark cnt=10/s)
800 counts/sec response to
signal
Hence the signal from a single molecule is easily
detectable with reasonable equipment.
But … Noise Budget for
Single-Molecule Detection
Nominal Band-Pass Filter
Transmission Performance:
In-Band = 0.5
Out-of-Band = 1E-6
Fraction of Excitation Light scattered
by Sample:
(Extremely clear sample)
0.1%:
3e15 Photons/s
Fraction of scattered Excitation
collected by Receving optics:
2%:
6E13 Photons/s
Fraction of collected Excitation
passed by Fluorescence Filter:
1e-6:
6E7 Photons/s
Hence, only one photon in 75,000 will be from the target Molecule!
Even with very careful blank subtraction, will need several thousand
molecules for detection, and samples must be very clear.
Why not just add another Fluorescence filter?
If the excitation rejection was increased from 1E-6 to 1E-12, then the
excitation leakage counts would fall below the dark count.
When this is tried, the rejection ratio goes from 1E6 to 0.5E-6 – an improvement factor of 2!
Dual Emission
Filters
The extra filter also reduces the signal by a factor of
2, so there is no improvement in SNR.
What is going on?
The Problem is Scatter:
In a good optical system, only ~99% of the light follows the
predicted paths – the rest scatters from surfaces and bulk at
random angles.
A low-probability ray path through the optics:
When light is incident on an interference filter at an
angle away from the normal, the bandpass of the filter
shifts toward shorter wavelengths; Hence:
•The excitation light that scatters through the filter at an
angle away from normal is not attenuated because it is
now in the shifted bandpass of the filter!
•Adding another filter does not help, because its
bandpass is also shifted for the high-angle scattered light.
Typical Performance for Fluorometer Filters:
Filters for Texas Red dye molecule:
• Max excitation wavelength: 596nm
• Max emission wavelength: 615nm
Fluorescence Filter
0o incident angle
Excitation Filter:
0o incident angle
Mutual
Rejection ~10-6
Off-Axis Performance of Fluorometer Filters:
At 26 degrees incident angle, the emission filter passes the excitation
light with no attenuation, as the bandpasses overlap completely!
Fluorescence Filter
0o incident angle
Excitation Filter:
0o incident angle
Fluorescence Filter
26o incident angle
The Wavelength-Spatial Filter Chain:
Spatial Filter
Wavelength
Filter
Spatial Filter
Wavelength
Filter
The Spatial Filter removes light that is not following the ray-trace
predicted path – hence removes the excitation light that “snuck”
through the shifted bandpass of the blocking filter.
When wavelength filters are interleaved with spatial filters,
the blocking ratios multiply and it is possible to get ANY
desired blocking ratio.
 Fluorescent samples can be read without blank
subtraction and without regard for turbidity.
Details, Details …
1. Many light sources (e.g., lasers) emit broad-band light at a level
~1E-6 below the narrow-band main emission; Hence the source
should also be filtered with a wavelength-spatial filter chain.
2. Spatial filters can be made compactly:
• Disks of black honeycomb material work well.
• Special holographic spatial filters are available only a few
mm thick.
3. Both wavelength and spatial filters work best when the sample
volume is small, and the ray angles through the optics can be
constrained to a narrow range.
Commercial Instruments that have used
(some of) this principle
1. Field-Portable Polarization Fluorometer (Jolley
Instruments -- now bankrupt).
2. Bio-Chip Scanner (Nanogen – never commercialized).
3. Reading fluorescent tags in saliva samples for drug testing
(company failed, but instrument achieved 1e-17+
rejection of excitation light).