Coming into focus

Biologists have discovered how to incorporate probes such as green fluorescent protein into living cells, allowing them to watch developments over many cell generations. Imaging these probes and tracking their behavior over time within the 3-D cell framework is still a difficult proposition, however. For one thing, researchers want to minimize exposure of the living cells to excessive light, which can cause photobleaching of the fluorophore and overall photodamage to cell health. The greater technical challenge is the difficulty of getting a sharply focused image of the tiny subcellular components the researchers study. One solution is a hybrid optical-digital imaging technique called wavefront coding.

To image tiny cellular structures, biologists use very-high-resolution optical microscopes. Unfortunately, such systems suffer from reduced depth of field. Typically, an immersion objective with a high numerical aperture (NA = 1.4) will have a lateral resolution of roughly 300 nm and a depth of field of approximately 700 nm. Features that extend several micrometers in depth, such as cell nuclei, will not all be in focus in a traditional wide-field microscope image. To address this problem, researchers have worked over the past two decades to develop microscopes that in some fashion reject out-of-focus blur and produce images that represent an optically sectioned view of some thin region within the depth of the cell. The instruments include confocal, wide-field deconvolution, multiphoton, and structured-illumination microscopes.

Such tools allow the biologist to sharply image fine structure, but only from a narrow depth of field in each image. To record and visualize information from throughout the cell volume, they acquire stacks of images from different focus steps. For many live-cell imaging applications, however, there is not enough time to acquire a multi-focus stack before the object moves or the fluorescent dye bleaches.

Our approach to this overriding problem of limited depth of field in high-NA optics is to use an integrated optical-digital systems design technique known as wavefront coding (see oemagazine, January 2002, p. 42).¹ The technique is based on the premise that specialized optics allow more object information to be encoded and preserved in a digitally recorded image. We modify a traditional microscope by inserting a custom phase plate (an optical element with an aspheric surface) into one of the slots near the back aperture plane of the objective. This blurs the acquired images, but it renders them insensitive to focus-related aberrations (defocus, spherical aberration, astigmatism, or field curvature). In terms of linear systems theory, the point spread function (PSF) and the modulation transfer function (MTF) become invariant with respect to defocus. A fast, single-iteration digital processing step produces a final image with an extended depth of field.

It is possible to configure a range of microscope objectives and CCD cameras to get similar results. Most standard modes of microscopy, such as bright-field, fluorescence, phase-contrast, or Hoffman-modulation-contrast, can be adapted for wavefront coding using standard white-light or arc-lamp illumination.

Figure 1. Adding a phase plate (left) to the system results in this PSF (center) and normalized 2-D MTF (right); the color bar represents increasing strength of the normalized spatial frequencies. Unlike a conventional microscope for which the MTF shrinks and produces zeroes with defocus, this element's PSFs and MTFs maintain their shapes over several micrometers of defocus.

The challenge of maintaining the high-spatial-resolution characteristics of high-power microscope objectives, while increasing their depth of field, has led to the design and testing of several optical element shapes. One such design has a surface variation that is in the f (r) cos(w θ+Φ) phase function family, where r and θ are the radius and angle in polar coordinates, and w and Φ are both constants (see figure 1).

If we Fourier transform the PSF of this sample wavefront-coded system, the resulting 2-D MTF shows the energy—the spatial frequency information—spread fairly symmetrically around each region of a circle. Here, the color bar indicates spatial-frequency strength with the maximum energy occurring in the center (lowest spatial frequency) and decreasing outward to the edge of the circle (the highest resolvable spatial frequency of this microscope system).

This MTF conforms closely to the size and circular symmetry that would be obtained using the same microscope system in a conventional (non-wavefront-coded) mode at best focus. The significance of the wavefront-coded system is that its MTF stays virtually the same when the focus is changed over an extended depth, whereas the conventional system MTF rapidly shrinks in diameter with defocus and shows nulls at some frequencies. This invariance of a wavefront-coding MTF with defocus (and absence of nulls) is why a single digital-image-processing step can reconstruct the extended-depth image. Furthermore, the near-circular MTF symmetry of this example wavefront-coding-element design means that object features extending in all directions in a microscope image will be equally well resolved.

The advantages of such an extended-depth microscope are apparent for biological time-lapse imaging of spatially varying fluorescent cell structures. For example, the extended-depth microscope needs to acquire only one image at each time interval, whereas sectioning-type microscopes may need 10 or more image acquisitions to obtain similar depth of field. When a biologist performs a time-lapse experiment acquiring hundreds of images over several hours, cutting the number of images by 90% considerably reduces photobleaching or photodamage to live cells. Conversely, if the goal is to track subcellular components that are rapidly moving in depth, the extended-depth microscope can record this information at video rates or faster, provided there is enough signal from the specimen; in comparison, the multi-focus stack acquisition process of sectioning microscopes would prove too slow.

Figure 2. Images show 0.5-µm-diameter fluorescent beads at different depths in a sample. Traditional microscope images (top) show that beads from each different focal depth are only sharp in one corresponding image plane. The extended-depth system (bottom) shows all beads clearly in all image planes. All, taken with Zeiss 63X, NA = 1.4 objective at 1-µm focus steps using the high-resolution mode of a Zeiss Axiocam CCD camera (scale: 10 µm).

We have installed a wavefront-coding phase element similar to that described above in a commercial biological microscope and imaged 0.5-µm-diameter fluorescent beads. If we use a traditional microscope to image the sample in 1-µm steps, beads from several different planes go in and out of focus. Using wavefront coding, we can generate well-resolved, extended-depth microscope images (see figure 2). The greatest challenge to the wavefront-coding system occurs when the object signal is very weak, resulting in a lower signal-to-noise ratio in the acquired image data. The same is true of conventional microscopy, but the digital processing step in wavefront-coding microscopy tends to increase the problem.

Figure 3. Traditional bright-field image of two cervical cells (top left) shows blurred region. A wavefront-coding image of the same sample shows all parts of the cells sharply (top right) but includes more noise; both images taken with a Zeiss 63X, NA = 1.4 objective (scale: 20 µm). A lower-magnification image of a dandelion leaf shows more blur for a traditional image (bottom left) compared to the sharper, but higher-noise extended-depth image (bottom right); both images taken with an Olympus 5X, NA = 0.1 objective with 1.5X intermediate magnifier (scale: 200 µm).

Figure 4. Bright-field microscopy images of packing material taken at focal positions 160-µm apart with traditional (top) and extended-depth configuration (bottom) show that portions of the traditional images are blurred at each focus position, while the images for the wavefront-coding system remain sharp. Images were taken using an Olympus 5X, NA = 0.1 objective, 1.5X intermediate magnifier and Cooke Sensicam CCD camera (scale: 200 µm).

Comparing standard bright-field images versus wavefront-coding, extended-depth images of human cervical cells, typical of Pap smear screening applications, shows how background noise can increase along with the increase in depth of field (see figure 3). The lateral resolution of the wavefront-coding image is, however, equivalent to that of the traditional bright-field image.

The wavefront-coding microscope works for applications outside biology, as well. Low-magnification images of closed-foam packing material, typical of the magnification and resolution needed for many industrial inspection applications, have nearly the same noise and lateral resolution in the extended-depth images as in the standard images (see figure 4).

Wavefront coding has opened the way for emerging applications such as the rapid acquisition of sharp images of 3-D moving objects such as MEMS devices and processes in living cells. Traditional techniques show blurring that would mask much of the depth information. By integrating the optics and digital signal processing into the original design process, we can obtain much more information from a microscope. oe

Further reading:

A. Baron and V. Chumachenko, IVD Technology, 8[9], 47-51 (2002).