2.1.

Theoretical Analysis of DOF

The DOF of an optical system is defined as the axial range in the object space where the object is imaged with an acceptable deterioration.¹¹ There are two different types of DOF which contribute to the system DOF: geometric and diffractive. The geometric DOF is the axial range in the object space within which the blurred spot on the image space cannot be distinguished by the detector. It can be calculated by the following formula:¹¹

The diffractive DOF is based on the light intensity distribution along the optical axis. The image deterioration is considered to be acceptable if the intensity does not fall below 80% of the maximum. The corresponding distance can be computed as follows:¹¹

Thus, for a realistic microscopic imaging system, both geometrical and diffractive effects exist simultaneously. The calculation of the total DOF has been thoroughly discussed in the last several decades.^11–16 Although a standard method of determining the total DOF has not been established to date, the following method is the most recommended in this field to compute total DOF, which is the sum of the diffractive and geometric DOF:^11–14

2.2.

Measurements of DOF

During the microscopic imaging process, the contrast of the captured image decreases when the object is moved away from the focal plane.^17,18 Measuring the contrasts at specific spatial frequencies is often performed in an effort to assess the microscopic image system.^19–21 Accordingly, in this study the DOF of the microscopic system was investigated experimentally by measuring the contrast at in-focused and off-focused positions. The DOF can be estimated experimentally by determining the range where the contrast is larger than 80% of its maximum.¹⁷

In order to acquire digital images, we modified a conventional microscope by installing a time delay integration (TDI) detector that enables obtaining a pixel size of 7 μm in one dimension. The microscope is also equipped with two different objective lenses providing the magnification power of $60\times$ (dry, $\mathrm{NA}=0.95$) and $100\times$ (oil, $\mathrm{NA}=1.25$), respectively.

During the experiment, the DOF range was estimated separately when applying each of the above two objective lenses. The experiment was divided into three steps. First, we measured the modulation transfer function (MTF) to determine the spatial frequency for DOF estimation. MTF was accomplished by measuring the image contrast at a series of discrete spatial frequencies from 0 to the system-resolving limit, with the measured contrast values normalized for the final MTF curve. Second, according to the MTF curve, the frequency where the contrast drops to half of the maximum was selected to estimate the DOF. Finally, at the selected frequency, the contrast was measured to determine the system DOF.

In order to determine the spatial frequency of a DOF estimation, the MTF was first measured using standard resolution targets. Two different bar pattern targets were used in the experiments. The USAF1951 resolution target contains different bar patterns with discrete spatial frequencies up to $645\mathrm{lp}/\mathrm{mm}$ (USAF1951, Edmund Optics, NJ). Another target with maximal frequency of $2000\mathrm{lp}/\mathrm{mm}$ was also applied to measure the contrast at spatial frequencies higher than $645\mathrm{lp}/\mathrm{mm}$ when it is necessary (MRS-4, Geller Microanalytical Laboratory, MA.).

For each microscopic objective lens, the MTF was estimated through measuring the contrast at different spatial frequencies from 0 to the resolving limit. In this investigated system, the pixel size of the camera is smaller than half of the resolving limit. Therefore, the spatial resolution is determined by the following formula:¹¹

In the MTF measurement, the test target was placed on the stage. The system was manually adjusted to ensure that the target is imaged at the in-focused condition. After that, the target was captured and the contrast of each pattern on the target was calculated by the following formula:²²

After the spatial frequency was determined, the DOF range was estimated for each objective lens. This was accomplished using the above test bar pattern targets. Before the measurement, the target was placed on the stage and the in-focused position was visually adjusted and determined. Then, starting from this in-focused position, the stage was gradually moved up and down with a series of steps. At each position, the target image was obtained by the detector and the contrast of the image is computed by Eq. (5). Finally, the calculated contrast was curved as a function of focusing positions. The range where the contrast is larger than 80% of the maximum is determined as the system DOF estimation.

2.3.

Evaluation of the DOF Impact on the Cytogenetic Image Qualities

In this study, we selected multiple pathological specimen slides that cover a variety of clinical samples acquired from bone marrow, blood, amniotic fluid, and products of conception (POC). These collected samples were all prepared using the standard clinical procedure. The digital images were then acquired from these specimen slides’ regions of interest (ROIs) to assess the impact of the microscope’s DOF on the cytogenetic image qualities. Since the resolving power of the $60\times$ and $100\times$ objective lenses are 0.353 μm and 0.268 μm, respectively, which provides enough meaningful information for clinical diagnosis, all the cytogenetic images were captured under these two $60\times$ and $100\times$ objective lenses in this study. Each ROI depicted an analyzable metaphase or interphase cell and each ROI was imaged at nine different positions, including the focal plane and the other positions away from the focal plane.

3.1.

DOF Theoretical Results

The theoretical results calculated by Eq. (3) in Sec. 2.1 are tabulated in Table 1. The one-dimensional (1-D) pixel size of the CCD detector used in this system is 7 μm. When applying a dry $60\times$ ($\mathrm{NA}=0.95$) microscopic objective lens and an oil-emerged $100\times$ ($\mathrm{NA}=1.25$) objective lens, the computed system DOF are 0.855 and 0.703 μm, respectively. As expected, using higher magnification power results in a smaller DOF.

Table 1

The depth of field of our microscopic scanning system equipped with two different objective lenses.

3.2.

DOF Experimental Measurement

Two example images of the USAF1951 resolution test bar target are demonstrated in Fig. 1(a) and 1(b), which were captured at the focal position and 3.5 μm away from the focal plane of an oil-emerged $100\times$ objective lens, respectively. The image in Fig. 1(b) was acquired at the off-focused state, as it is obviously blurred. Figure 2 illustrates two measured MTF curves of the microscope when using two $60\times$ and $100\times$ objective lenses separately. Based on the measured MTF, the MTF decreases approximately to its half maximum value at 456 and $645\mathrm{lp}/\mathrm{mm}$, respectively. These spatial frequencies were therefore used to estimate the system DOF when the $60\times$ and $100\times$ objective lenses were applied.

Fig. 1

Sample images of an USAF 1951 standard resolution target, acquired using a $100\times$ (oil, $\mathrm{NA}=1.25$) objective lens including (a) in-focused image, (b) blurred image acquired 3.5 μm away from the focal plane.

Fig. 2

The measured MTF curve for the tested microscope using (a) $60\times$ (dry, $\mathrm{NA}=0.95$) objective lens and (b) $100\times$ (oil, $\mathrm{NA}=1.25$) objective lens.

The “half-maximum” contrast measurements, plotted as a function of focusing positions, are shown in Fig. 3(a) and 3(b), when the $60\times$ and $100\times$ objective lenses were used, respectively. For each curve, the contrast value reaches its maximum at the in-focused position (0 at $x$-axis), and decreases as the target is moved away from the in-focused position. As mentioned, the DOF can be estimated as the range where the contrast is higher than 80% of its maximal value.¹⁷ Therefore, the actual measured system DOF are 3.0 μm and 1.8 μm when applying the $60\times$ and $100\times$ objective lenses, respectively.

Fig. 3

The measured “half-maximum” contrast values versus focusing positions for the tested microscope using (a) $60\times$ (dry, $\mathrm{NA}=0.95$) objective lens and (b) $100\times$ (oil, $\mathrm{NA}=1.25$) objective lens.

As predicted by theoretical calculations, the results reveal that the DOF decreases when increasing the NA Due to the experimental restriction, the measured DOF is substantially greater than the theoretical prediction. In the experiment, we could not directly measure the size of the image spot or the axial light intensity for the geometrical and diffractive DOF separately. Alternatively, the DOF was estimated by measuring the image contrast. But the $z$-position where the image contrast drops to 80% of the maximum is not exactly the same position for the geometrical or diffractive DOF. In other words, theoretical computation can only be used as a reference.

3.3.

DOF Impact on Diagnosis of Clinical Cytogenetic Images

The microscopic images of analyzable cells acquired from four pathological samples including bone marrow, blood, amniotic fluid, and POC are shown in Figs. 4 to 11 as examples. Figures 4 to 6 are metaphase cells acquired by the microscopic system using a $60\times$ (dry, $\mathrm{NA}=0.95$) objective lens, and Figs. 7 to 10 are metaphase cells acquired under $100\times$ (oil, $\mathrm{NA}=1.25$) objective lens. Figure 11 illustrates an interphase cell captured under a $100\times$ (oil, $\mathrm{NA}=1.25$) objective lens. In each of Figs. 4Fig. 5 to 6, Image (a) was obtained at the focal plane resulting in clear and sharp chromosome band patterns, which are adequate for clinical diagnosis. Image (b) was acquired 1 μm out of focus, and the band patterns are as clear as Image (a). When the cell was obtained 1.5 μm away from the focal plane, the image is somewhat blurred but still recognizable, as shown in Image (c). The band contrast decreases more significantly when the cell moves further away from the focal plane, with the band shapes becoming barely recognizable and then totally unrecognizable in Image (d) and (e), both of which were acquired 2 and 2.5 μm out of focus, respectively.

Fig. 4

Microscopic images of a clinically analyzable cell contained in a bone marrow sample, captured using a $60\times$ objective lens (dry, $\mathrm{NA}=0.95$), at positions of (a) in-focused, (b) 1 μm, (c) 1.5 μm, (d) 2 μm, and (e) 2.5 μm away from the focal plane.

Fig. 5

Microscopic images of a clinically analyzable cell contained in a blood sample, captured using a $60\times$ objective lens (dry, $\mathrm{NA}=0.95$), at positions of (a) in-focused, (b) 1 μm, (c) 1.5 μm, (d) 2 μm, and (e) 2.5 μm away from the focal plane.

Fig. 6

Microscopic images of a clinically analyzable cell contained in a POC sample, captured using a $60\times$ objective lens (dry, $\mathrm{NA}=0.95$), at positions of (a) in-focused, (b) 1 μm, (c) 1.5 μm, (d) 2 μm, and (e) 2.5 μm away from the focal plane.

Fig. 7

Microscopic images of a clinically analyzable cell contained in a bone marrow sample, captured using a $100\times$ objective lens (oil, $\mathrm{NA}=1.25$), at positions of (a) in-focused, (b) 0.5 μm, (c) 1 μm, (d) 1.5 μm, and (e) 2 μm away from the focal plane.

Fig. 8

Microscopic images of a clinically analyzable cell contained in a blood sample, captured using a $100\times$ objective lens (oil, $\mathrm{NA}=1.25$), at positions of (a) in-focused, (b) 0.5 μm, (c) 1 μm, (d) 1.5 μm, and (e) 2 μm away from the focal plane.

Fig. 9

Microscopic images of a clinically analyzable cell contained in a POC sample, captured using a $100\times$ objective lens (oil, $\mathrm{NA}=1.25$), at positions of (a) in-focused, (b) 0.5 μm, (c) 1 μm, (d) 1.5 μm, and (e) 2 μm away from the focal plane.

Fig. 10

Microscopic images of a clinically analyzable cell contained in an amniotic fluid sample, captured using a $100\times$ objective lens (oil, $\mathrm{NA}=1.25$), at positions of (a) in-focused, (b) 0.5 μm, (c) 1 μm, (d) 1.5 μm, and (e) 2 μm away from the focal plane.

Fig. 11

Microscopic fluorescent in situ hybridization (FISH) images of a clinically analyzable interphase cell contained in a POC sample. The chromosomes of interest are marked as the fluorescent dots, and the cell is captured by the system under investigation using $100\times$ objective lens (oil, $\mathrm{NA}=1.25$), at positions of (a) in-focused, (b) 1 μm, and (c) 2 μm away from the focal plane.

In Figs. 7 to 10, the band sharpness decreases at a faster rate as compared with those shown in Figs. 4 to 6. In Figs. 7 to 10, Image (c) was obtained 1 μm away from the focal plane, which shows a cell containing somewhat recognizable band shapes with decreased contrast. However, these cells are still suitable for clinical practice. Furthermore, when the image was obtained 2 μm out of focus, the band patterns become completely unrecognizable and unsuitable for diagnosis purposes, as illustrated in Image (e).

Figure 11 shows a typical image of an interphase cell acquired from a POC sample. This cell was processed by the fluorescence in situ hybridization technique (FISH) biomarkers. The diagnostic genome fragments are demonstrated as bright dots in the captured image. The cell in Fig. 11(a) was imaged at the focal plane, and shows two clear green dots on the blue background. When the cell was moved 1 μm away from the focal plane, as shown in Fig. 11(b), the dots become smaller but still recognizable. However, the dots disappear completely in Fig. 11(c), which was captured 2 μm out of focus.

In summary, these experimental and observation results agree with the measured DOF ranges demonstrated in Sec. 3.2. For the investigated microscopic system, the range of DOF is approximately 3.0 μm and 1.8 μm when applying $60\times$ (dry, $\mathrm{NA}=0.95$) and $100\times$ (oil, $\mathrm{NA}=1.25$) objective lenses, respectively. The images acquired within DOF illustrate clearly cytogenetic features, which are adequate for the diagnosis of diseases in clinical practice. However, when the cell is moved out of the DOF range, the pathological meaning of the acquired images slowly diminishes.