IVIV

Practical Aspects of Lens DesignPractical Aspects of Lens Design

October 2008October 2008

Rudi Rottenfusser – Carl Zeiss MicroImaging

The Objective

The Most Important Microscope Component

Lenses

Glass Parameters (excerpt)

• Refractive Index• Dispersion• Thermal Expansion Coeff.• Spectral Transmission• No Autofluorescence• No Schlieren, bubbles, inclusions• Reflectivity• Film Adhesion (AR coatings)• Chemical Resistance • Resistance to Humidity• Availability

Topics

• Airy Disk / Point Spread Function• Resolution Criteria – Rayleigh, Sparrow, etc.• Definition: Depth of field / focus

• Aberrations

• The Objective – What do the markings mean– What to consider when selecting an objective

• Website - References

What happens to the image of the object when it travels through the various microscope components?

1) No Lens Aberrations (“perfect lens”)

On Axis image

Wave fronts

In phase ½λ Out of phase

NA: 0.4 0.8 1.3

Relative sizes of Airy disk (D) as a function of Numerical Aperture

DD

D

Airy Disk

D = Diameter of Airy disk in image

plane ObjectiveNAD

22.1

D

Resolution in z as defined by the “Airy Body” is

ObjectiveNAD

22.1

2NA

nz

Airy Disk

ObjectiveNAd

61.0

Rayleigh Limit of Lateral Resolution

d = ½ D

D

• Minimum distance dmin is reached, when the principal maximum of object 1 (center of Airy Disk) coincides with first minimum of object 2

• Intensity of maxima =

20% higher than intensity of “dip” between maxima

Intensity

Xdmin

Two points at minimum distance to be “resolved”

ObjectiveNAd

61.0Rayleigh Limit of

lateral resolutiond = ½ D (radius)

Airy Disks of 2 clearly imaged separate points:

Rayleigh Criterion for resolution

Objectives - Definitions: Depth of Field / Focus

Example: C-Apochromat 40x/1,2W 1 Rayleigh unit = 0,42 µm in object plane

= 0,668 mm in image plane

eNAM

n

NA

nT

2

T = Depth of field (µm)

λ = Wavelength (µm)n = Refractive IndexM = Magnification (Image Ratio)e = diffraction-limited resolution

d in image plane (µm)From Shinya Inoué / Kenneth R. Spring book: “Video Microscopy Fundamentals - 2nd edition”Chapter 2.4.6

Different formulas (e.g. Berek 1927, Shillaber 1944, Françon 1961, Martin 1966, Michel 1981, Piller 1977)

In general: At high NA the depth of field is small and the depth of focus at the image side is large. This reverses at low magnifications!

What happens to the image of the object when it travels through the various microscope components?

2) Considering Aberrations

• Spherical Aberration

• Chromatic Aberration (axial)

• Chromatic Aberration (lateral or radial)

• Curvature of Field

• Astigmatism

• Distortion

• Internal Reflexes

Aberrations

Plan-Apochromat 40x/0.95 corr.

Correction Collar set at 0.21mm

Spherical Aberration

Plan-Apochromat 40x/0.95 corr.

Correction Collar set at 0.17mm

Spherical Aberration

Spherical Aberration

Infinite number of prisms with different angles

and, therefore, different refractive

powers

Due to the spherical character of the lens, rays do not cross over at the same Focal

Point

Spherical Aberration

Spherical Aberration is reduced by smaller aperture

Less confused “Zone of Confusion”

Fixing Spherical Aberration

Multiple Elements

Aspheric Lens

Exaggerated

Reducing Spherical Aberration

How to generate Spherical Aberration:

Incorrect Cover Glass

Maxim

um

Inte

nsi

ty in a

n

image o

f a p

oin

t obje

ct

How to generate Spherical Aberration:

Incorrect Cover Glass

Reso

luti

on [

µm

]

(Fu

ll W

idth

, H

alf

Max)

Use 0.170 mm thick cover slips !

Types and Thickness Ranges

No.0 ......... 0.08 - 0.12 mm

No.1 ......... 0.13 - 0.17 mm

No.1.5....... 0.16 - 0.19 mm

No.2 ......... 0.19 - 0.23 mm

No.3 ......... 0.28 - 0.32 mm

No.4 ......... 0.38 - 0.42 mm

No.5 ......... 0.50 - 0.60 mm

Choose the right cover glass!

No.1.5....... 0.16 - 0.19 mm

40x/1.3 Oil immersion objective – Energy at different depths of penetration z in water

How to generate Spherical Aberration:

Focusing deeper into the sample

Aquaeus Medium

Water Immersion

Benefit of Water Immersion

Objectives (with cover slip correction)

Cover Slip n=1.52

n~1.3

n~1.3

Chromatic Aberration (Axial)

Remember “Dispersion” of Light!

Fixing Chromatic Aberration

The classic “Achromat” (Doublet)

n ≈ 1.55 n ≈ 1.65

Objectives - Definitions:

Corrected Wavelength (nm):

UV VIS IR

Plan Neofluar - - (435) 480 546 - 644 - -

Plan Apochromat - - 435 480 546 - 644 - -

C-Apochromat 365 405 435 480 546 608 644 - -

IR C-Apochromat - - 435 480 546 608 644 8001064

Objectives - Best Focus

1 RU

480 nm546 nm

644 nm

RU = Rayleigh Unit

Image

Lateral Chromatic Aberration (LCA)

(Chromatic Magnification Difference)

Lateral Chromatic Aberration (LCA)

Lateral Chromatic Aberration (LCA)

Different manufacturers correct for LCA in different ways:

Leica:The tube lens corrects for a fixed amount of LCA

Nikon:The objectives themselves are fully corrected

Olympus:The objectives themselves are fully corrected

Zeiss:The tube lens corrects for objectives with different LCA’s

Sagittal

Tan

gen

tial

Astigmatism

Spherical Aberration

Astigmatism

Coma

Intensity Distribution

in Airy Disk

Curvature of field: Flat object does not project a flat image

(Problem: Camera Sensors are flat)

f1

image

object

f2

Objectives - Definitions: Flatness

Flatness at 435nm:

SF 18 SF 25

Plan Neofluar 1 R

Plan Apochromat < 0,5 R

C-Apochromat 0,6 - 1 R 1 - 2R

Distortion

Pincushion

Barrel

Internal Straylight

% R

[nm]400 700

4

2Anti Reflection (AR) Coating

uncoated

Single layer

Multi layer

Reflexes (unwanted reflections)

~ 1%

~ 0.1%

Internal Straylight

How does it work?

Anti-Reflex (AR) Coating

/4

Questions?

Objective Markings

Thread Diameter0.8”x1/36” (RMS) 27mm, 25mm

Mounting Distance (Specimen to Flange):22, 45, 60, 75mm, others?

..1.2589254.101010R

“Standard” Sequence

Magnification

1.251

1.252

1.253

1.254

1.255

1.256

1.257

1.258

1.259

1.2510

1.2511

=

=

=

=

=

=

=

=

=

=

=

1.25x

1.6x

2x

2.5x

3.2x

4x

5x

6.3x

8x

10x

12.5x…

Why these strange numbers?

What to consider when selecting an objective:

1. Magnification

2. Working Distance

3. Numerical Aperture (NA) – Resolution / Depth of Field

4. Image Quality – minimized Aberrations (spherical, chromatic, flatness of field, astigmatism, coma, distortion)

5. Adaptation to specific Applications (Contrasting Techniques, Cover Slips, Chambers, Shape of front lens for Access)

6. Spectral Transmission (Visible,IR,UV?)

7. No Autofluorescence

8. No Strain (Pol)

9. Temperature Tolerance

10. Temperature Isolation (heating!)

11. Chemical Resistance

12. Electrical Shielding

13. Minimal Path Gradient (2-photon)

14. Perfect Parfocality and Parcentricity

15. Compact yet durable

16. Inexpensive

For a comprehensive lookup of objectives, consult Websites!(Example for Zeiss: www.zeiss.com/campus)

Description of Classes of Objectives

Example (Screenprint)

Please refer to appropriate web sites from

Leica

Nikon

Olympus

Thank you, and do enjoy your microscopes !

Rudi Rottenfusser

Office: 508/289-7541

Cell: 508/878-4784

Email: rrotte@mbl.edu

Microscopy Support: 800/233-2343

Imaging Support: 800/509-3905

Website: www.zeiss.com/micro

Educational Site: www.zeiss.com/campus