Microscope objective

A microscope objective is the multi-element lens nearest the specimen. It collects light from the sample and, together with a tube lens, forms a magnified image on a camera or at the eyepiece. Its two headline numbers are engraved on the barrel: the magnification and the numerical aperture, as in 10×/0.25, 40×/0.65 or 100×/1.40 Oil. The NA, more than the magnification, decides what the microscope can resolve and how much light it gathers; a 40×/0.65 objective resolves about 0.50 µm at 532 nm, and a 100×/1.40 oil objective about 0.24 µm at 550 nm.

Magnification and tube length

Modern objectives are infinity corrected: a point on the specimen leaves the objective as a collimated beam, and a separate tube lens of focal length $f_\text{tube}$ brings it to focus on the image plane. The magnification is

$$M = \frac{f_\text{tube}}{f_\text{obj}} .$$

Manufacturers use different tube lens focal lengths (200 mm, 180 mm and 165 mm are all in use), so the engraved magnification holds only with the maker's own tube lens. A 20× objective designed for a 200 mm tube lens has $f_\text{obj}$ = 10 mm; a 20× designed for 180 mm has 9 mm, and in a 200 mm system it gives 22.2×. The collimated space between objective and tube lens is where filters, beam splitters and dichroic mirrors go without shifting the focus. Total visual magnification is the product of objective and eyepiece: 40× with a 10× eyepiece gives 400×.

Resolution and NA

For incoherent imaging the radius of the Airy disk, and the Rayleigh resolution, is

$$r = \frac{0.61\,\lambda}{\text{NA}} .$$

At 532 nm this is 1.30 µm for NA 0.25, 0.81 µm for NA 0.40 and 0.50 µm for NA 0.65. Dry objectives top out near NA 0.95. Immersion raises the limit by filling the space between lens and coverslip with a liquid: water ($n$ = 1.33) or oil ($n$ = 1.515), where an NA of 1.40 corresponds to a half-angle of 67.5° in the oil. The diffraction limit entry treats the Abbe and Rayleigh forms in detail. Light collection rises roughly as NA², which is why fluorescence and confocal microscopy favor high-NA objectives even at modest magnification.

Working distance, coverslips and labels

The working distance is the clearance between the front lens and the specimen or coverslip. It shrinks as NA rises: a few millimeters to over 10 mm for low-power dry objectives, and roughly 0.1–0.2 mm for a 100× oil objective.

Objectives for biological work are corrected for a coverslip 0.17 mm thick, engraved as "/0.17"; "/0" means no coverslip and "/–" means the objective is insensitive to it. With a dry objective of high NA, a coverslip of the wrong thickness adds spherical aberration that broadens the focus and dims it; correction collars let the user compensate. Other common engravings:

• Achromat: chromatic aberration corrected at two wavelengths, the basic grade.
• Fluor or semi-apochromat: better color correction, with fluorite or similar glass.
• Apochromat (Apo): color corrected at three or more wavelengths, usually with the highest NA for its magnification.
• Plan: corrected for field curvature, so the whole field is in focus at once on a flat camera sensor.

Focusing a laser with an objective

Objectives are also standard tools for focusing a laser to a small spot or coupling it into a single-mode fiber or chip waveguide. For a collimated Gaussian beam of $1/e^2$ radius $w_\text{in}$, the focused waist is $w_0 \approx \lambda f_\text{obj}/(\pi w_\text{in})$. To match the 5.2 µm mode radius of standard single-mode fiber at 1550 nm with a 10 mm focal length objective, the input beam should be about 1.9 mm in $1/e^2$ diameter; with a 20 mm focal length (10× on a 200 mm system), about 3.8 mm. The fiber mode diverges with a half-angle of only about 0.095 rad, so an objective of NA 0.25 or more does not clip it, and the input beam size sets the spot. The resulting coupling efficiency is limited by mode overlap, the objective's transmission, and aberrations at the laser wavelength.

Pitfalls

• Many visible objectives have reduced transmission and degraded correction in the near infrared; objectives designed for the NIR exist for 1064 nm and telecom work.
• The entrance pupil diameter of an infinity objective is about $2 f_\text{obj}\,\text{NA}$: 8 mm for a 20×/0.40 on a 200 mm system. A laser beam much smaller than the pupil does not use the full NA and focuses to a larger spot.

Common questions

What do the numbers on a microscope objective mean?

For example "Plan Apo 60×/1.40 Oil ∞/0.17": plan and apochromat correction, 60× magnification, NA 1.40 with oil immersion, infinity corrected, for 0.17 mm coverslips. A working distance is often engraved as well.

How is the focal length of an objective found?

Divide the tube lens focal length the objective was designed for by its magnification: a 40× objective for a 200 mm tube lens has $f$ = 5 mm.

Why does a higher NA give better resolution?

The objective captures diffracted light out to larger angles, which carries finer spatial detail, so the Airy radius $0.61\lambda/\text{NA}$ shrinks. The image is formed from what passes through the objective's back focal plane, the pupil whose radius is $f_\text{obj}\,\text{NA}$.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017); M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999); J. B. Pawley (ed.), Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).