The X-Y-Zs of Biomedical Imaging

Kevin McCarthy

At the heart of many biomedical instruments lies an automated digital microscope. While many digital microscopes employ simple bright-field imaging using epi (through-the-objective) illumination, variants include transmissive illumination, fluorescence microscopy, dark-field illumination, total internal reflection fluorescence (TIRF), Nomarski, confocal, and other techniques. In all of these cases, some simple optical rules can be used to optimally configure a system for each application. These rules, in turn, drive the requirements for the system’s mechanics. This article explores how the optics and mechanics interact in biomedical imaging systems and explains how to optimize imaging throughput.

Determining Optical Resolution

The first step toward configuring an optical system for a biomedical application is to determine how much optical resolution the system needs. For example, a simple mammalian cell-counting application might work well with a resolution of 2 µm, while a pathology application targeting fine structural morphologies of cell nuclei might require resolution down to 0.35 µm. A key property of any microscope objective is its numerical aperture (NA), which is the sine of the half angle of the cone of light passing through the objective. The proper NA for an application is equal to 0.5 λ/R, where λ is the wavelength of the illumination (typically 0.5 µm) and R is the desired resolution in the same units. Thus, the cell-counting application would require an NA of only 0.12, while the pathology application would require an NA of 0.70.

Once the NA has been calculated, the objective’s magnification is no longer a free variable. The higher the NA, the higher the objective’s magnification will be. Typical NA ranges for microscope objectives are 4X: 0.1 to 0.2; 10X: 0.25 to 0.4; 20X: 0.4 to 0.8; and 40X and 60X: 0.65 to 0.95. In general, higher-NA objectives for a given magnification are more expensive than lower-NA objectives, but they also provide higher resolution.

Assuming a required resolution of 0.4 µm and a 20X, 0.70-NA objective, the next choice is to determine whether the objective has finite conjugates or is infinity corrected. If such optical elements as a beamsplitter or a fluorescent filter cube are not needed between the objective and the sensor, a finite conjugate objective with a typical tube length of 160 or 210 mm can be used. However, if an optical element is needed between the objective and the sensor, an infinity-corrected objective and a tube lens are required between the last optical element and the sensor. While tube lenses typically have unity magnification capability, other powers are also available, allowing users to tweak the overall magnification. The total magnification equals the objective magnification times the tube lens magnification.

Field of View

After the user has chosen the magnification, the field of view (FOV) at the biological sample can be addressed. FOV is determined by dividing the imaging sensor size by the magnification. For example, if the image sensor measures 10 mm square and the magnification is 20X, the FOV will be 0.5 mm square. A typical biological sample—whether the canonical 25 × 75-mm glass slide, a tissue section, or a custom flowcell—will be many times larger than this field of view.

A programmable XY stage allows users to sequentially image many small fields of view across the total area of the sample while moving quickly from one FOV to the next. It isn’t practical to take a single giant image because image sensor costs soar as they get larger. In addition, microscope objectives are at most corrected for a 25-mm image diameter (the diagonal of a 17.7-mm-square image sensor).

The function of the XY stage is twofold. It accurately moves from one FOV to the next as rapidly as possible and then settles quickly at the new FOV. Any residual vibration must be well under the optical resolution. As soon as the stage has settled to within the range of optical resolution, image exposure begins. When image integration is complete, the stage jumps to its new FOV, while the digital camera downloads the image to the host. Minimally, the travel of the XY should equal the length and width of the sample, although additional travel may be required to permit sample loading and unloading.

Configuring the XY Stage

There are several ways to configure the XY stage with varying levels of performance. For low-throughput applications, a stepper motor and a leadscrew are adequate. Time must be budgeted after the end of each move for the high-Q ringing of the payload mass and nut/bearing compliance to damp out. Direct-drive stages with linear servo motors and linear encoders provide the highest levels of performance. For a typical FOV of 0.75 mm, a direct-drive stage such as the Dover MMG series can move and settle to under 0.5 µm in about 50 milliseconds. Depending on the integration time of the digital camera and the illumination intensity, this movement time enables users to acquire as many as 16 images per second. The actual (not empty) resolution of the XY stage must be several times finer than the optical resolution. If the magnification is 20X and the numerical aperture is 0.70, the stage resolution should be at least 0.1 µm. Images can also be acquired during constant velocity scanning. Again, direct-drive stages provide the highest levels of performance.

The image sensor consists of millions of individual pixels. A good rule of thumb is to choose a pixel size so that the optical resolution corresponds to between 1 and 2 pixels at the image sensor. To determine the pixel size, resolution is multiplied by magnification. Thus, with a 20X magnification, a numerical aperture of 0.70 NA, and resolution of 0.4 µm, the sensor pixel is 8 µm. In such cases, sensor pixels ranging in size from 4 to 8 µm would be suitable.

The next task is to ensure that the sample is precisely focused. To accomplish this step, it is necessary to calculate the depth of field (DOF), which is defined as the distance along the optical axis that the sample can be moved from a state of precise focus and still be able to fully resolve fine sample details. Assuming a given NA and the presence of air between the objective and the sample, the DOF is:

where λ is the wavelength of light (typically 0.5 µm). In almost every case, an automated Z axis objective positioner is required to maintain focus across the sample. For such low-NA systems as 4X, 0.15-NA objectives, the depth of field amounts to 22 µm. In such cases, a simple leadscrew-based stage or even a cam is suitable for moving the objective into precise focus. For such high-NA systems as a 20X, 0.80-NA apochromatic objective, the depth of field is only ±0.48 µm, requiring a higher level of stage performance. With 5-nm resolution, direct-drive stages such as the MMG are more than sufficient for such applications.

Configuring the Z Axis

The final task is to know what position to command of the Z axis to ensure precise focus. For thin samples, users can employ a continuous-tracking laser autofocus system that is directed down through the objective using a beamsplitter. Such a system can detect the reflection off the underside of a coverslip, whereby an optical coating on the coverslip surface can be designed to pass visible light while strongly reflecting the infrared wavelength of the laser autofocus. For thick samples, the user may have to acquire images at multiple planes within the sample and then choose the image with the highest contrast.

Budget permitting, the ultimate technique for increasing image throughput is to add additional cameras. Figure 1 shows the objective end of a system with four 20X, 0.80-NA objectives on a 36-mm pitch. Capable of capturing and processing 350 million pixels per second, this system features four cameras, each of which is mounted on its own direct-drive focus axis and has its own continuous-tracking laser autofocus.

Conclusion

A complex procedure, image acquisition of biological samples is increasingly required in a variety of diagnostic tools. Establishing the right workflow requires developing close collaboration across several technical disciplines. But if users follow some simple rules to ensure that both the optic and mechanical design elements align with the application requirements, they will be well on their way to a successful project.

Kevin McCarthy is CTO of Boxborough, MA–based Dover Medical & Lab Automation. He has more than 30 years of experience in optimizing imaging applications. He can be reached at [email protected].