Apodized Phase Contrast

Halo Reduction with Apodized Phase Contrast

Differences in light absorption are often negligible between the various intracellular components and plasma membranes in living cells, rendering them barely visible when observed through the microscope utilizing the classical technique of brightfield illumination. Phase contrast microscopy takes advantage of minute refractive index differences within cellular components and between unstained cells and their surrounding aqueous medium to produce contrast in these and similar transparent specimens.

Figure 1 - Phase Contrast Light Pathways

Light passing through a ring aperture or annulus, mounted in the substage condenser front focal plane, is used to illuminate the specimen in conventional phase contrast microscopy (Figure 1). As the hollow cone of light emanating from the phase annulus encounters the transparent specimen, it is either diffracted by subcellular components and the membrane or passes through undeviated. Light that passes through the specimen undeviated arrives at the rear focal plane of the objective in the shape of a ring, whereas the fainter light diffracted by the specimen is spread over the entire surface of the focal plane. A small phase shift measuring approximately one quarter wavelength relative to the direct light is induced in the light diffracted by the specimen.

The phase differences of the direct light from the background and the diffracted light from the specimen cause the two beams to interfere with each other at the intermediate image plane. This is achieved by adding or subtracting a quarter wave shift to the direct light by means of a semi-transparent phase plate strategically placed in a plane that is conjugate (the objective rear focal plane) to the annulus in the condenser (the condenser front focal plane). The direct background light is attenuated by a neutral density thin film applied to the phase ring in the objective. At the intermediate image plane, an interference pattern results, which produces intensities proportional to the phase shift induced by the specimen.

An unfortunate artifact in phase contrast microscopy is the halo effect, which results in spurious bright areas around phase objects or reverse contrast in images. This effect is especially prevalent with specimens that induce large phase shifts. Reducing the halo artifact was once thought to be a difficult theoretical problem, but recent advances in objective phase ring configuration have resulted in a new technique termed apodized phase contrast (Figure 2), which allows structures of phase objects having large phase differences to be viewed and photographed with outstanding clarity and definition of detail.

Figure 2 - Anodized Phase Plate Configuration

Presented in Figure 2 are a conventional (or classical) and an apodized phase plate positioned at an angle to the viewer and sectioned through the center for ease of illustration. The classical phase plate on the left, which is positioned at the objective rear focal plane, has a thin ring of neutral density material (termed a phase film) applied to the surface (also illustrated in Figure 1). The purpose of the film is to retard the phase of direct light passing through the specimen by one quarter wavelength to allow constructive and destructive interference with diffracted light at the intermediate image plane. On the right in Figure 2 is an illustration of an apodized phase plate. Surrounding the phase film in this plate are two concentric areas of semi-transparent neutral density material, which reduce the intensity of light diffracted from the specimen at small angles. In apodized phase contrast microscopy, this phase plate replaces the plate on the left at the objective rear aperture.

The effect of apodized phase plates on images seen in the microscope is illustrated in Figure 3 for two specimens. Figure 3(a) is a photomicrograph of a starfish embryo taken with a Nikon Eclipse E600 microscope operating in standard phase contrast mode. The objective used was a long working distance (LWD) Ph1 DL (dark-light) designed to produce a dark image outline on a light gray background. This type of objective is the most popular type for routine phase contrast examination of cells and other living material, because it produces the strongest dark contrast in objects having major differences in refractive indices. Note the halo surrounding the outer periphery of the embryo and the lack of contrast and image detail present in the central portion of the cell mass. A significant improvement in contrast is observed with the use of a corresponding objective having apodized phase plates, as illustrated in Figure 3(b). In this figure, the starfish embryo has a dramatically reduced halo around the periphery and exhibits sharper edges with enhanced internal specimen detail and apparent depth of field.

Figure 3 - Halo Reduction in Apodized Phase Contrast

A similar pair of photomicrographs is illustrated in Figure 3(c) and 3(d), using a live euglena specimen. Euglenas are a member of the protozoan order Euglenida, a remarkable group of single-celled creatures, many of which exhibit characteristics of both plants and animals. Figure 3(c) presents a classical phase contrast image taken of the euglena specimen using a DL phase objective. Internal specimen details have a vague contrast and the outer cellular membrane is surrounded by a substantial halo. When the same specimen is imaged using apodized phase optics (Figure 3(d)), the halo size is reduced and internal specimen features are more highly resolved.

Apodized Phase Contrast Theory

The refractive index (n) of most phase objects, especially living cells, ranges between 1.36 and 1.37 when illuminated with light having an average wavelength centered in the visible region of the spectrum (550 nanometers). For specimens that have a spherical geometry, the phase difference between the specimen and the surrounding medium increases as the specimen thickness grows larger, resulting in a smaller diffraction angle for light deviated by the specimen. Assuming a spherical specimen, the maximum phase difference (δ) and diameter (d) are related by the following equation:


δ = (2Π/λ)(n' - n)d

where λ is the wavelength of light in a vacuum (or in air), n' is the refractive index of the specimen, and n is the refractive index of the surrounding medium (usually a buffered aqueous solution). It is evident from the equation that increasing the specimen diameter (d) will illicit a correspondingly larger phase difference (δ) in the illumination wavefront, provided the refractive indices of the specimen and media remain constant.

Now, we will consider the diffraction pattern produced by a circular aperture of diameter d. In the ideal case, when the objective is aberration-free and provides a uniform circular aperture, two adjacent points are just resolved when the centers of their Airy disks are separated by a distance r, the central Airy disk radius. The quantity r is determined by the equation:


r = 0.61λ/n(sin(Θ))

where λ is the wavelength of light with air as the immersion medium and θ is the angle of diffraction (aperture angle). For this discussion, we assume that the aperture diameter equals the resolution distance r, and can then state:


r = d = 0.61λ/n(sin(θ))

which rearranges to:


sin(θ) = 0.61λ/nd

Substituting equation (1) into equation (4) yields:


sin(θ) = (2π/λ)(n' - n)0.61λ/nδ


sin(θ) = 2π(n' - n)0.61/nδ

If the diffraction angle (θ) is small, then there is an inverse relationship between the term sin(θ) and the phase difference (δ):


sin(θ) ∝ 1/δ

In order to examine the diffracted and undeviated light intensity at the intermediate image plane, we must first consider the physical aspects of the illuminating wavefronts. If the illuminating wavefront is a uniform plane wave, then the incident wavefront (φ(0)) and the wavefront after passing through a phase object (specimen; φ(1)) can be described by the following equations:


φ(0) = sin(ωt)


φ(1) = sin(ωt + δ)

where ω is the angular frequency of the illuminating wavefront, t is time, and δ is the relative phase difference between the wavefronts passing through the specimen or through the surrounding media. In most cases the value for δ is small, so that equation (9) reduces to:


φ(1) = sin(ωt) + δcos(ωt)

The first term in equation (10) describes the incident light wave (equation (8)) and represents the undiffracted or direct light passing through and around the specimen, while the second term indicates the sum of the light diffracted by the specimen. In most cases, the diffracted light has a quarter wave phase difference with respect to the direct light, and an amplitude that is proportional to the phase difference caused by the specimen. Taking into account the addition (or subtraction) of one quarter wavelength from the direct portion of the light through the utilization of an appropriate zonal phase shift plate at the objective rear focal plane, equation (10) reduces to:


φ(1) = (1 + δ) cos(ωt)

To arrive at the intensity (I) of the wave at the intermediate image plane, we can take the square of equation (11) and integrate to remove the time dependency:


I = (1 + δ)2

The image intensity is proportional to (1 + δ)2 because the integral of the squared cosine is a constant. Thus, the relationship between the diffraction angle, the amplitude of light diffracted by the specimen, and the phase difference have been established. From equation (12), it is obvious that the intensity of light at the intermediate image plane is proportional to the sum of the amplitudes of the direct and diffracted light. It should be noted that the diffracted light intensity varies with field position, while direct light is uniform across the image plane.

Apodized Phase Plates

In practice, halo reduction and an increase in specimen contrast can be obtained by the utilization of selective amplitude filters located adjacent to the phase film in the phase plates built into the objective at the rear focal plane. These amplitude filters consist of neutral density filter thin films applied to the phase plate surrounding the phase film as illustrated in Figure 2. The transmittance of the phase shift ring in the classical phase plate is approximately 25 percent, while the pair of adjacent rings surrounding the phase shift ring in the apodized plate have a neutral density with 50 percent transmittance. The width of the phase film in both plates is the same. These values are consistent with the transmittance values of phase shifting thin films applied to standard plates in phase contrast microscopes.

Figure 4 - Diffraction Angles in Anodized Phase Plates

The necessary width of the surrounding neutral density films can be calculated by the diffraction angle (θ), discussed in equations (2) through (7). This value is somewhat specimen-dependent, but commercial apodized phase objectives available from Nikon are fabricated assuming an object (specimen) diameter of approximately 10 microns, a typical value for biological cells used in tissue culture experiments.

Basic principles of the apodized phase contrast technique are presented in Figure 4, which illustrates the effects of both small and large specimens. The relationship between the phase difference in specimens of various sizes heavily influences the attenuation effects of apodized phase plates. A generous portion of the light diffracted by larger specimens (greater than or equal to 10 microns in diameter; Figure 4(a)) passes through the neutral density absorption rings and will be attenuated, thus reducing the intensity. On the other hand, for specimens that are smaller than 10 microns in diameter, such as nucleoli, plasma membranes, and cytoplasmic granules, diffracted light will pass on the outer periphery of the neutral density filter rings because of the large diffraction angle. In this case, the amplitude of diffracted light will not be attenuated by the transparent portion of the phase plate, rendering specimen details in high contrast (but with associated halos).

The apodization technique has been used successfully with other optical configurations to reduce the intensity of direct light at the aperture. In any diffraction-limited imaging system, the point spread function usually has side-lobes or side-rings of significant intensity. These artifacts can be of considerable concern in systems designed to resolve a weak light point-source that is positioned adjacent to a stronger point-source. The term apodize is derived from the Greek word meaning "to remove the feet". In optical terms, the "feet" are considered to be the side-lobes or side-rings in a diffraction-limited imaging system. A similar technique, commonly employed in digital imaging, is known by the term windowing.

In general terms, apodization of an optical system requires the introduction of amplitude attenuation (or in some cases, enhancement) to light passing through the exit pupil. The amount of attenuation is usually negligible in the center of the pupil, but increases with radius and becomes greatest at the edges of the pupil near the aperture. In other words, the edges of an image at the aperture can be "softened" by the introduction of a light-attenuating mask. Because diffraction at an abrupt aperture results in edge waves originating at the rim, the softening effect helps to spread the apparent origin of the diffracted waves over a broader area. This results in a suppression of the ringing effects induced by the edge waves.

Apodization has classically been utilized to provide a tapering of transmittance near the edges of light traveling through the exit pupil of an optical system in order to suppress the intensity of side-lobes surrounding the point spread function. In recent years, however, apodization has been applied to other systems and used to describe any introduction of absorption into the exit pupil, regardless of whether the side-lobes are suppressed or accentuated.

In conclusion, the utilization of apodized phase contrast optics results in dramatically improved images, which have reduced halos and high contrast in minute specimen detail. In most cases, subcellular features (such as nucleoli) can be clearly distinguished as having dark contrast with apodized objectives, but these same features have bright halos or are imaged as bright spots using conventional phase contrast optics. With the apodized optics, contrast is reversed due to the large amplitude of diffracted light relative to that of the direct light passing through the specimen.

The contrast of the image from a phase object can be altered by modulating the transmittance and size of the annular neutral density zones surrounding the central phase film. If these zones are produced with a gradient of transmittance, then object contrast can be more closely controlled for a large variety of specimen sizes.

Contributing Authors

Tatsuro Otaki - Optical Design Department, Instruments Company, Nikon Corporation, 1-6-3 Nishi-Ohi, Shinagawa-ku, Tokyo, 140-8601, Japan.

Charles D. Howard and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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Apodized Phase Contrast