7.29 Optical Instruments
265
7.29.3 Phase-Contrast Microscope
As many biological cells are mostly transparent, their structures are difficult to see in
an ordinary microscope. In 1934, in order to increase the contrast of images of living
cells without using dyes, the Dutchman Frits Zernike invented the ‘phase contrast
microscope’. He knew that the indices of refraction in the cell and its transparent
structures are slightly greater than that of water, so that the speed of the light is
slightly less while passing through these structures. This causes the phase of light
waves from the illuminator to be retarded after traveling through the cell, and thus
slightly shifted back in phase relative to the illumination outside the cell. Moreover,
the illuminating light refracted by passing through the cell is dispersed to greater
angles than the background light passing through the media surrounding the cell, so
that light dispersed by the cell can be separated from the background light.
Suppose a plane wave from an illuminator in the microscope passes through a
mostly transparent specimen. After passing, the wave will have a change of phase
that depends on the variations in the index of refraction in the object. In complex
number notation, the new wave will be proportional to A(x, y) = exp (iφ(x, y)),
where (x, y) are locations in the plane just past the specimen. Note that the intensity
of this light, proportional to A ∗ A, will have no phase variation. The fact that the
specimen’s index of refraction differs only slightly from the background water
means that φ is small, so that exp ((iφ) ≈ 1 + iφ.
To get the phases of the wave to cause an intensity variation, Zernike used
a quarter-wave plate 47 to shift the phase of the separated background waves by
−90 ◦ = −π/4 radians. Recombining the phase-shifted background waves (whose
amplitude of 1 changed to exp(−iπ/4)) with the specimen-dispersed waves in
effect changes A ≈ 1 + iφ into A = −i + iφ. This makes the intensity of the
light depend on phase variations: A ∗ A ≈ 1 − 2φ, and the image now has light and
dark regions depending on the index of refraction variations. The phase term can be
enhanced relative to the background term by having some absorption in the quarterwave plate, so that the amplitude of the background light is changed by transmission
with a factor a exp (−iπ/2), where the absorption coefficient a 2 is less than one. On
recombination with the separated specimen light, the new light intensity becomes
proportional to a 2 − 2aφ. The ratio of the phase-contrast term to the direct term is
−2φ/a, so the phase term is enhanced by a factor 1/a compared to a non-absorbing
case when a = 1. Of course, this also means the overall intensity is reduced by a 2 ,
so there is a playoff of enhanced phase contrast with reduced overall intensity. Color
fringes should also be expected when white light rather than one color is used.
47 A quarter-wave plate is constructed by depositing a thin dielectric film onto a glass plate. The
dielectric causes the phase of the light of the selected wavelength to shift back by 90 ◦ . Adding a
little metal to the film causes an additional absorption.
265
7.29.3 Phase-Contrast Microscope
As many biological cells are mostly transparent, their structures are difficult to see in
an ordinary microscope. In 1934, in order to increase the contrast of images of living
cells without using dyes, the Dutchman Frits Zernike invented the ‘phase contrast
microscope’. He knew that the indices of refraction in the cell and its transparent
structures are slightly greater than that of water, so that the speed of the light is
slightly less while passing through these structures. This causes the phase of light
waves from the illuminator to be retarded after traveling through the cell, and thus
slightly shifted back in phase relative to the illumination outside the cell. Moreover,
the illuminating light refracted by passing through the cell is dispersed to greater
angles than the background light passing through the media surrounding the cell, so
that light dispersed by the cell can be separated from the background light.
Suppose a plane wave from an illuminator in the microscope passes through a
mostly transparent specimen. After passing, the wave will have a change of phase
that depends on the variations in the index of refraction in the object. In complex
number notation, the new wave will be proportional to A(x, y) = exp (iφ(x, y)),
where (x, y) are locations in the plane just past the specimen. Note that the intensity
of this light, proportional to A ∗ A, will have no phase variation. The fact that the
specimen’s index of refraction differs only slightly from the background water
means that φ is small, so that exp ((iφ) ≈ 1 + iφ.
To get the phases of the wave to cause an intensity variation, Zernike used
a quarter-wave plate 47 to shift the phase of the separated background waves by
−90 ◦ = −π/4 radians. Recombining the phase-shifted background waves (whose
amplitude of 1 changed to exp(−iπ/4)) with the specimen-dispersed waves in
effect changes A ≈ 1 + iφ into A = −i + iφ. This makes the intensity of the
light depend on phase variations: A ∗ A ≈ 1 − 2φ, and the image now has light and
dark regions depending on the index of refraction variations. The phase term can be
enhanced relative to the background term by having some absorption in the quarterwave plate, so that the amplitude of the background light is changed by transmission
with a factor a exp (−iπ/2), where the absorption coefficient a 2 is less than one. On
recombination with the separated specimen light, the new light intensity becomes
proportional to a 2 − 2aφ. The ratio of the phase-contrast term to the direct term is
−2φ/a, so the phase term is enhanced by a factor 1/a compared to a non-absorbing
case when a = 1. Of course, this also means the overall intensity is reduced by a 2 ,
so there is a playoff of enhanced phase contrast with reduced overall intensity. Color
fringes should also be expected when white light rather than one color is used.
47 A quarter-wave plate is constructed by depositing a thin dielectric film onto a glass plate. The
dielectric causes the phase of the light of the selected wavelength to shift back by 90 ◦ . Adding a
little metal to the film causes an additional absorption.