ECEN 4616/5616Optoelectronic Design

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Lecture #22: 3/05/14

Designing a 10X Microscope Objective

Eyepiece

Objective

Tube

“Standard” Microscope Layout:

First, what does a ’10x’ objective mean?

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.

Condenser

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 ObjectiveKnowing 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

l l’

u u’

Well, we still don’t know what focal length lens we need, but we have enough information to do a paraxial layout:

We also know that: 195 & 10

17.727, 177.272

ll ll

l l

Hence:

And from the imaging equation: 1 1 1l f l

We can calculate the focal length: 16.116f mm

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, where is the cutoff spatial frequency of the objective.2

xNA 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

ll’

u u’h

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:

1 1sin 0.25 , tan( ) tan sin 0.25 0.258u u

(0.258)( 17.727) 4.573hu h mml

The F/# of the lens, therefore is: # 1.762fFh

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 ObjectiveRevised Paraxial Layout – Two Lenses

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:

d0 d2

u0u2

u1

h1h2

d1

K1

K2

1 00 2tan sin 0.25 0.258, =- =-0.0258 (both unchanged)

10uu u

1 20 1 2 2

0 2

, 2.58 , , 4.386h hu h mm u h mmd d

2 11

1

0.1204h hud

u1 is not far from the average of u0, u2 (0.116), so the job of refracting the marginal ray is fairly evenly divided between the lenses.

1 0 2 11 2

1 2

0.0533, 0.0333u u u uK Kh h

1 218.75 , 30f mm f mm

And the F/#s are 3.6 and 3.42

d0 l’d1

f1

f2

Designing a 10X Microscope ObjectiveRevised Paraxial Layout

Just listing the values that go into Zemax:• d0 = 10 mm• f1 = 18.75 mm (dia=5.16, F#=3.6)• d1 = 15 mm• f2 = 30 mm (dia=8.8, F#=3.4)• l’ = 170 mm

The F#s are now reasonable for achromats

Zemax Reality Check

Designing a 10X Microscope ObjectivePicking 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 ObjectivePicking Glasses

Designing a 10X Microscope ObjectiveZemax 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 ObjectiveStarting 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

-R1

R2

The power and the surface curvatures are related by the ‘thin len formula’:

1 2( 1)( )K n c c

1 21 2 1 2

1 2 1 2

, VK V KK K K K and KV V V V

Designing a 10X Microscope ObjectiveStarting Solutions for Zemax

Using the Paraxial Achromat construction equations:

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 mmf2 = -13.995 mm

R1 = 9.9004R2 = -345.9Diameter: 6mm

Achromat #2:(f = 30 mm)f1 = 12.822 mmf2 = -22.392 mm

R1 =15.8407R2 = -553.44Diameter: 9mm

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?)Achromat 1:

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 ObjectiveStarting 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 ObjectiveStarting 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 ObjectiveReversing 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 ObjectiveReversing a Lens

And the Spherical Aberration looks to be much better corrected:

Designing a 10X Microscope ObjectiveZemax 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 ObjectiveZemax 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 ObjectiveZemax 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 ObjectiveZemax 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 ObjectiveZemax 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: 9.6mmLens spacing: 5mmMagnification: -13

The MTF is not too bad:

Designing a 10X Microscope ObjectiveZemax 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

SourceSource Filter

Sample

Fluorescence Emission Filter

Detector

Sample Fluoresces in all directions

Collected fraction of fluorescence light

Optical Stop

Signal Budget for Single-Molecule Detection Fluorometer

(Assumptions are for typical dye like Texas Red)

Light from source:(One at sample)

1mW @ 596 nm photons/sec

Response per dye molecule:(Peak emission @ 615nm) ≈ 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

2mm 18103IQF

Hence the signal from a single molecule is easily detectable with reasonable equipment.

But … Noise Budget forSingle-Molecule Detection

Nominal Band-Pass Filter Transmission Performance:

In-Band = 0.5Out-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.

Dual Emission Filters

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 1E-6 to 0.5E-6 – an improvement factor of 2!

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.

Filters for Texas Red dye molecule:• Max excitation wavelength: 596nm• Max emission wavelength: 615nm

Excitation Filter: 0o incident angle

Fluorescence Filter0o incident angle

Mutual Rejection ~10-6

Typical Performance for Fluorometer Filters:

Excitation Filter: 0o incident angle

Fluorescence Filter26o incident angle

Fluorescence Filter0o incident angle

At 26 degrees incident angle, the emission filter passes the excitation light with no attenuation, as the bandpasses overlap completely!

Off-Axis Performance of Fluorometer Filters:

The Wavelength-Spatial Filter Chain:

Wavelength Filter

Wavelength Filter

Spatial FilterSpatial 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).