IV Practical Aspects of Lens Design October 2008

1. IVPractical Aspects of Lens DesignOctober 2008 Rudi Rottenfusser – Carl Zeiss MicroImaging

2. The Most Important Microscope Component The Objective

4. Lenses

5. 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

6. 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

7. What happens to the image of the object when it travels through the various microscope components? 1) No Lens Aberrations (“perfect lens”)

8. On Axis image Wave fronts

9. ½λ Out of phase In phase

10. Relative sizes of Airy disk (D) as a function of Numerical Aperture D D D NA: 0.4 0.8 1.3

11. Airy Disk D D = Diameter of Airy disk in image plane

12. Airy Disk Resolution in z as defined by the “Airy Body” is D Rayleigh Limit of Lateral Resolution d = ½ D

13. Intensity X dmin Airy Disks of 2 clearly imaged separate points: Rayleigh Criterion for resolution • 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 Two points at minimum distance to be “resolved” Rayleigh Limit of lateral resolution d = ½ D (radius)

15. Objectives - Definitions: Depth of Field / Focus Different formulas (e.g. Berek 1927, Shillaber 1944, Françon 1961, Martin 1966, Michel 1981, Piller 1977) T = Depth of field (µm) λ = Wavelength (µm) n = Refractive Index M = 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 Example: C-Apochromat 40x/1,2W 1 Rayleigh unit = 0,42 µm in object plane = 0,668 mm in image plane 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!

16. What happens to the image of the object when it travels through the various microscope components? 2) Considering Aberrations

17. Aberrations • Spherical Aberration • Chromatic Aberration (axial) • Chromatic Aberration (lateral or radial) • Curvature of Field • Astigmatism • Distortion • Internal Reflexes

18. Spherical Aberration Plan-Apochromat 40x/0.95 corr. Correction Collar set at 0.21mm

19. Spherical Aberration Plan-Apochromat 40x/0.95 corr. Correction Collar set at 0.17mm

20. Spherical Aberration Infinite number of prisms with different angles and, therefore, different refractive powers

21. Spherical Aberration Due to the spherical character of the lens, rays do not cross over at the same Focal Point

22. Spherical Aberration is reduced by smaller aperture Less confused “Zone of Confusion”

23. Fixing Spherical Aberration

24. Reducing Spherical Aberration Multiple Elements Aspheric Lens Exaggerated

26. How to generate Spherical Aberration: Incorrect Cover Glass Maximum Intensity in an image of a point object

27. How to generate Spherical Aberration: Incorrect Cover Glass Resolution [µm] (Full Width, Half Max)

28. Choose the right cover glass! 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 No.1.5....... 0.16 - 0.19 mm

30. How to generate Spherical Aberration: Focusing deeper into the sample 40x/1.3 Oil immersion objective – Energy at different depths of penetration z in water

31. Benefit of Water Immersion Objectives (with cover slip correction) Water Immersion n~1.3 Cover Slip n=1.52 Aquaeus Medium n~1.3

32. Chromatic Aberration (Axial) Remember “Dispersion” of Light!

33. Fixing Chromatic Aberration n ≈ 1.65 n ≈ 1.55 The classic “Achromat” (Doublet)

34. Objectives - Definitions: l Corrected Wavelength (nm): UVVISIR Plan Neofluar - -(435)480546-644 - - Plan Apochromat - -435480546-644 - - C-Apochromat 365 405 435480546608644- - IR C-Apochromat - -4354805466086448001064

35. 1 RU Objectives - Best Focus RU = Rayleigh Unit 480 nm 546 nm 644 nm

36. Lateral Chromatic Aberration (LCA)(Chromatic Magnification Difference) Image

37. Lateral Chromatic Aberration (LCA)

38. 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

39. Astigmatism Tangential Sagittal

40. Intensity Distribution in Airy Disk Spherical Aberration Astigmatism Coma

41. Curvature of field: Flat object does not project a flat image (Problem: Camera Sensors are flat) f1 f2 image object

42. 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

43. Distortion Pincushion Barrel

44. Internal Straylight

45. Reflexes (unwanted reflections) % R 4 uncoated Anti Reflection (AR) Coating 2 Single layer ~ 1% Multi layer ~ 0.1% 700 400 l [nm]

46. Internal Straylight

47. Anti-Reflex (AR) Coating How does it work? l/4

48. Questions?

49. Objective Markings Thread Diameter 0.8”x1/36” (RMS) 27mm, 25mm Mounting Distance (Specimen to Flange): 22, 45, 60, 75mm, others?

50. Magnification “Standard” Sequence Why these strange numbers?