2.1.

New Optical Imaging System Design

The design of a digital imaging optical system with high performance detection of biological sample slides and biochips centers around the image quality, including the consideration of the resolution, zoom, aberration, and optical transfer functions, each of which can be optimized by using rays tracing calculations. All parameters of optical system structure, including the surface curvature radius of every lens, the thickness, the material used, the separation distance, and the surface aperture, were varied to obtain an excellent optical specificity and image quality, including high resolving power, appropriate zoom, low aberration, and high optical transfer functions. The functional relationships between the specificity, image quality, and structural parameters of the system can be described as follows:

Based on this optical design method, an optimum digital imaging optical system structure for the detection of biochips is shown in Fig. 1 and the contents listed in Table 1 . The optical imaging system is composed of a set of objective and magnifying lenses. The objective set is a combination of seven lenses including two doublets, and uses only three glass materials, ZF2, ZK7, and ZK11. The objective has a high numerical aperture of 0.72 for collecting the signal from the object, a focal length of $13.06\mathrm{mm}$ , and a front focal length of $3.22\mathrm{mm}$ to provide a working distance of approximately $3\mathrm{mm}$ . There is a parallel ray path between the objective and the magnifying lenses, to which it is convenient to also add filters and other optical elements. The magnifying lenses consist of five lenses with one set of doublets. This optical system has a zoom of 2.26. Because of its high numerical aperture and long working distance, our developed optical imaging scanning system is convenient for use with biochips with paling height of about $0.8\text{to}2.0\mathrm{mm}$ . This long working distance provides space for materials on the chip surface, such as for the positioning of cells and tissue samples, even space for a thin layer of culture solution or a glass cover slip. In comparison, general microscopes with an objective with has a numerical aperture of 0.65 have a working distance of $<1\mathrm{mm}$ . This distance is not sufficient to accommodate high paling biochips, or cells and tissue samples under a culture solution or a cover slip.

Fig. 1

Optical structure design of the digital imaging optical system.

Table 1

Optimization of the digital imaging scanning system (units: mm).

2.2.

Analysis of the New Digital Imaging Optical System Design

In a fluorescence imaging system, the objective collected the emission fluorescence (em-fluor) bound on the biochip, as shown in Fig. 2 , which is ideally a spherical wave,

Fig. 2

Configuration of the objective collecting fluorescence.

The intensity of emission fluorescence is,

When a biochip is placed at the focal plane of the objective, and the objective has a numerical aperture $\mathrm{NA}=n\times \sin \theta$ , $tg\theta =r∕R$ , where $n$ is the refractive index, then Eq. 3 can be simplified as Eq. 4:

The optical specialty and aberration of our novel imaging system can be analyzed by using the optical design software ZEMAX-EE. The encircled energy diagram of our developed system is shown in Fig. 3 , where the horizontal coordinate is the radius, and the vertical coordinate is the normalized fraction of the enclosed energy. The encircled energy diagram is the percentage of total energy enclosed as a function of distance from either the chief ray or the centroid at the image of a point object, while the diffraction-limit curve is for the aberration free encircled energy computed on-axis. In Fig. 3, it can be seen that when using our developed digital imaging system, when an object with a height of $0.5\mathrm{mm}$ is set at the focal plane of the objective, then the efficiency of collected emission fluorescence from the object is near to the diffraction limit.

Fig. 3

The encircled energy diagram of the system.

The optical path difference (OPD) is a scalar quantity and is identical to the aberration in the tangential direction $PX$ and the sagittal direction $PY$ , respectively. The data plotted in Fig. 4a is the optical path difference of our digital imaging system, the vertical axis scale is one wave, and the horizontal scale is the normalized entrance pupil coordinate. The OPD maximum of our digital imaging system is smaller than one wave. The distortion is defined as the real chief ray height, minus the paraxial chief ray height, divided by the paraxial chief ray height, times 100. The distortion values of our digital imaging system are described in Fig. 4b, where the distortion values in a view field of $0.5\mathrm{mm}$ are smaller than 0.1 %, and the distortion values to four different wave lengths—530, 570, 620, and $670\mathrm{nm}$ —are identical. Figure. 4 shows that very little aberration and low distortion limits are hallmarks of our digital imaging system.

Fig. 4

Optical path difference and distortion of the system.

2.3.

Constitution of the Digital Imaging Scanning System

A new digital imaging scanning system was built by applying the prior optical design parameters (Fig. 5 ). A laser with a wavelength of $532\mathrm{nm}$ was used to irradiate the biochip on the $xy$ scanning stage by optical fiber coupled and collimated lenses, and a cut-off was used to control the exposure time and reduce the photobleaching from the laser irradiation. An attenuator was used to adjust the intensity of the irradiating beam to fit with the requirements of different biochip applications. The fluorescence of dye-tagged biological molecules on the biochip was induced and was collected initially by the objective set, then the fluorescence passed through a filter and was imaged on a video CCD (Watec Company Limited, Japan) by a magnifying lens set. Finally, the fluorescence image of the biological molecule on the biochip is transferred into the computer for digital image processing via an image card.

Fig. 5

The developed digital imaging scanning system.

As illustrated in Fig. 3, this system is an advanced digital imaging scanner for biochip applications characterized by an objective with a high numeral aperture of $\mathrm{NA}=0.72$ , a long working distance of $3\mathrm{mm}$ , and a high efficiency of collecting fluorescence near the diffraction limit. Because an oblique incident laser was used to excite the fluorescence from the biochip, there was very little dark-field irradiation emanating from the background of reflected incident laser light. Generally, an oblique incident beam produces an uneven ellipse spot on the incident plane, shown in Figs. 6a, 6b, 6c , but the oblique incident beam in our digital imaging scanning system was reshaped into an even round spot on the biochip by a cylinder lens set. The change of the incident spot after reshaping is shown in Figs. 6d, 6e, 6f. The cylinder lens set was specified as listed Table 2 . The power density distribution of the beam spot before and after reshaping is shown in Figs. 6c and 6f. Because fluorescence intensity is an approximately direct ratio to the power of the exciting beam spot, the even power density distribution of the reshaped beam spot will make a truer fluorescent image of the biochip.

Fig. 6

The reshaping of spots by an oblique incident beam.

Table 2

The mechanism and optical layout of the cylinder lens set (units: mm).

2.4.

Restructure Scanning Images

The system has been designed to detect an imaging area of $0.5\times 0.5\mathrm{mm}$ with high resolving power in one scan, as shown in Fig. 5. To obtain the large $20\times 60\text{-}\mathrm{mm}$ detection area of a whole biochip, an $xy$ scanning stage is used to move the biochip to obtain a large number of patched images at different positions, and then these patched images are restructured into a large combined image. Generally, large position errors and obviously joined traces tend to occur when a number of high resolution images are patched together. To correct for such join errors, an edge overlap restructuring algorithm was developed and is shown in Eq. 5. Here, $S_1(i,j)$ and $S_2(i,j)$ are two border patched images with a $16\text{-}\text{pixel}$ -wide edge overlap area, and $M$ and $N$ are two natural numbers.

When structuring a combined image from many patched images captured at different scanning positions, the process of restructuring patched images is as follows. First, two border patched images $S_1(i,j)$ and $S_2(i,j)$ were moved to meet the minimum $S_{\min }$ condition, and an optimal matching position for restructuring the patched images was calculated. Second, the patched images $S_1(i,j)$ and $S_2(i,j)$ are cut to remove the eight-pixel-wide edge area from each respective image, and then become two new (nonoverlapping) patched images $S_1^{\prime }(i,j)$ and $S_2^{\prime }(i,j)$ . Finally, two new patched images $S_1^{\prime }(i,j)$ and $S_2^{\prime }(i,j)$ are joined at the optimal matching position. Using this process, image by image, each of the patched images could be restructured into a large combined image. Last, a fine processing and smoothing of the images restores high image quality to the combined image end product. By employing this edge overlap restructuring algorithm for the rapid display of the restructured chip image, the position error can be reduced to $1\text{pixel}$ , which is about $3\mu \mathrm{m}$ in size, and is the minimum chip resolution of our image scanning system. Our system, however, has a $10\times$ zoom, and when used, the position error of $1\text{pixel}$ can be reduced to about $0.8\mu \mathrm{m}$ . Such high resolution images require significant computing power and storage capacity, and hence the restructured high resolution restructured image is displayed only very slowly. A comparison of restructured images with or without use of the edge overlap algorithm is shown in Fig. 7 . A large position error and obviously joined trace can be seen in Fig. 7a when the images were restructured without using the edge overlap algorithm. In contrast, Fig. 7b shows correction of position error of the patched images and no evidence of joined traces after the edge overlap algorithm was used.

Fig. 7

Comparison of the restructured images.

In the last decade, a number of image matching techniques for restructuring have been explored for use during image processing. Examples include area-based matching, which uses windows composed of gray values, and feature-based matching, which uses a-priori features extracted in each image.^{14, 15, 16, 17, 18, 19} There are some disadvantages to using the area-based matching method, including high sensitivity of the gray values to illumination intensity, and the large time taken and large search space needed for matching. There are several different feature-based matching methods, including the gradient across the edge scheme,¹⁵ the correlation scheme,^{16, 18} and the wavelet scheme.¹⁹ Feature extraction methods are often computationally complex and require both the definition of features and that many parameters are chosen a-priori.

To reduce the effect of the gray changes due to illumination intensity and to simplify the definition of the features, we explored the prior edge overlap restructured algorithm. This algorithm only performs a matching feature with minimal gray differences in the edge overlap area over a width of $16\text{pixels}$ . Except the a-priori choice of the $16\text{-}\text{pixels}$ -wide edge overlap area from our digital images, there are few other parameters requiring selection. Thus, the absence of complex calculations reduces the time needed for image patching and restructuring. Our developed edge overlap restructured algorithm has proved to be robust for restructuring our scanning patched images and is well suited for high resolution imaging of biochips.

2.5.

Automatic Discrimination of Positive Probes from Scanning Images and Analysis of the Data Matrix of Biochips

For biochip applications, not only is the scanner required to detect the biochip and obtain an image, but data need to be extracted from the scanning images for analysis of information based on the character of the signal spots of the probes arrayed on the biochip. An automatic algorithm was developed capable of discriminating positive probes, extracting information from the biochip images and for producing a data matrix analysis of all probes on the biochip. The algorithm can perform the tasks automatically by the following steps.

Step 1

Choose an optimum threshold value for the binary processing of images by use of the Otsu algorithm.¹² First, the gray-level histogram of digital images is defined as $PHS\left(s\right)$ , where $s$ is the gray level of pixels in digital images. The gray class average $\mu \left(K\right)$ and the gray class histogram $\omega \left(K\right)$ are defined respectively as,

Eq. 6

$$\mu \left(k\right)=\sum _{s=1}^k(s-1)PHS\left(s\right),$$

Eq. 7

$$\omega \left(k\right)=\sum _{s=1}^{k}PHS\left(s\right),$$

where $k$ is a natural number.

A class analyzing function is described as,

Eq. 8

$${\sigma }_B\left(k\right)=\frac{{[\mu \left(k\right)\omega \left(k\right)-\mu \left(k\right)]}^2}{\omega \left(k\right)[1-\omega \left(k\right)]}.$$

When the class analyzing function ${\sigma }_B\left(k\right)$ is maximum, an optimum threshold value $T$ for the binary images is obtained as $T=k-1$ . The binary processing of images is shown in Fig. 8 , where Fig. 8a is the original gray image, and Fig. 8b is the binary image with an optimum threshold value.

Fig. 8

The binary images processed with optimum threshold values.

Step 2

Calculate the center and the space of the columns and rows of the microarray probes on the biochip from the binary images.

If the binary images are described as a data matrix $S_{(m,n)}$ , then the center of the columns and rows of microarray probes can be positioned at the maximum of the gray sum of pixels along the horizontal direction and along the vertical direction as shown in Figs. 9a and 9b , where $n$ and $m$ are two natural numbers.

Fig. 9

The gray sum of pixels along the horizontal and vertical directions.

The sum of gray of all pixels in the vertical direction is

Eq. 9

$$\text{row}\left(\chi \right)=\sum _{y=1}^{n}S(x,y),y=1,2,\dots ,n.$$

The sum of gray of all pixels in the horizontal direction is

Eq. 10

$$\mathrm{col}\left(y\right)=\sum _{x=1}^{m}S(x,y),\chi =1,2,\dots ,m.$$

The space of the row probes can be calculated by using the maximum intensity spectrum of the Fourier transform of $\text{row}\left(x\right)$ in the vertical direction, and the space of column probes can also be calculated by using the maximum intensity spectrum of the Fourier transform of $\mathrm{col}\left(y\right)$ in the horizontal direction.

The Fourier transform of the gray sum of pixels along the vertical direction is

11.

$$F\left\{\text{row}\left(x\right)\right\}=F_{\text{row}}\left(p\right),$$

$$=\sum _{x=1}^m\text{row}\left(x\right)\exp [-j2\pi (p-1)(\chi -1)∕n],\text{where}x=1,2,\dots ,m.$$

The Fourier transform of the gray sum of pixels along the horizontal direction is

Eq. 12

$$F\left\{\mathrm{col}\left(y\right)\right\}=F_{\mathrm{col}}\left(q\right)=\sum _{y=1}^n\mathrm{col}\left(y\right)\exp [-j2\pi (q-1)(y-1)∕m],\text{where}y=1,2,\dots ,n.$$

The intensity spectrum of the Fourier transform along the vertical direction is ${\mid F_{\text{row}}\left(p\right)\mid }^2$ , and the intensity spectrum of the Fourier transform along the horizontal direction is ${\mid F_{\mathrm{col}}\left(q\right)\mid }^2$ , which are shown in Fig. 10 .

Fig. 10

Fourier transfer of the gray sum of images.

The frequency $f_{i\max }$ is obtained at the maximum intensity spectrum of the Fourier transform along the vertical direction. The frequency $f_{j\max }$ is obtained at the maximum intensity spectrum of the Fourier transform along the horizontal direction.

The space $d_i$ of the row probes is calculated as $d_i=1∕f_{i\max }$ .

The space $d_j$ of the column probes is calculated as $d_j=1∕f_{j\max }$ .

Step 3

Discriminate the signal spots of the microarray probes and produce their data matrix.

After this step, the center and the space of signal spots of the microarray probes from step 2 are considered, and the following process is then used to remove the noise and retain the effective spot signals for the calculation of the signal intensity of probes.

A normal circle disperse $ND\left(r_0\right)$ is defined as,

Eq. 13

$$ND\left(r_0\right)=\int 2\pi r^{2}dr∕\left(\pi r_0^2\right),$$

where $r_0$ is the radius of the probes, and generally

$$r_0⩽\frac{1}{8}\sqrt{d_i^2+d_j^2},$$

where $d_i$ is the space of the row probes, and $d_j$ is the space of the column probes.

An actual signal spot disperse $AD\left(L\right)$ is defined as:

Eq. 14

$$AD\left(L\right)=\frac{{\sum }_{i=1}^{l1}{\sum }_{j=1}^{l2}{(i^2+j^2)}^{1∕2}}{l1\times l2},$$

where $l_1$ and $l_2$ are two natural numbers,

$$L=\frac{1}{2}\sqrt{l_1^2+l_2^2}.$$

When $i=1\text{to}{l}_1$ and $j=1\text{to}{l}_2$ , $(l_1^2+l_2^2)∕4=r_0^2$ , then the signal intensity of spots is $S_{(i,j)}>0$ .

The ratio of the disperse $R{D}_{\mathrm{NA}}$ is calculated as:

Eq. 15

$$R{D}_{\mathrm{NA}}=AD\left(L\right)∕ND\left(r_0\right).$$

In an ideal circular probe signal spot, $R{D}_{\mathrm{NA}}=1$ . Typically, however, an actual signal spot image of biochip probes is an irregular circular spot, then $R{D}_{\mathrm{NA}}⩽1$ . In our actual scanning images of biochip probes, an experimental ratio of the disperse $R{D}_{\mathrm{NA}}$ was summarized as $0.5⩽R{D}_{\mathrm{NA}}⩽1$ , allowing the noise to be removed and the effective signals of the discriminated probe spots retained.

The center position and space of the retained effective signal spots can be calculated by using the center and the space of signal spots of microarray probes obtained in step 2. A grid of intersecting images can be obtained, as shown in Fig. 11a , and the effective signal spots of the biochip images are indicated in Fig. 11b. Image processing was then undertaken to remove the noise and keep the effective signal spots for the pseudocolor images shown in Fig. 11c. The average (or medium) signal intensity of these effective probes was calculated from the original scanning images of biochips with a radius $r_0$ . A signal data matrix of probes as shown in Table. 3 was obtained, which can be used to analyze and determine the positive or negative probes of biochips by an experimental threshold.

Fig. 11

Automatic target discrimination and pseudocolor processing.

Table 3

The analysis data matrix.

Row	Column
	1	2	3	4	5	6
1	141.04	179.19	160.28	157.85	183.01	171.74
2	0.00	0.00	0.00	0.00	0.00	0.00
3	125.63	133.38	178.93	166.23	130.40	141.10
4	98.20	112.60	118.52	114.04	117.84	117.20
5	0.00	0.00	0.00	0.00	0.00	0.00
6	149.87	125.37	174.10	174.06	153.19	176.15

Employing the previously developed algorithms for automatic discriminating of targets, all effective probes can be discriminated from the reconstructured and combined scanning images of the biochips. Thus, an experimental analysis data matrix from the DNA microarray or protein microarray can be obtained.

2.6.

Detection Sensitivity and Resolving Power of the System

The detection sensitivity of the newly developed digital imaging scanner was tested as shown in Fig. 12a , where a Full-Moon normal molecular density validated-biochip (Full Moon BioSystems, Sunnyvale, California) was used. The unit of density is the molecule number per square micron, and the signal is a relative intensity within the range of 0 to 250. In Fig. 12a, the molecule with density $0.561\text{fluors}∕\mu {\mathrm{m}}^2$ was detected with a signal of 45.39 where the signal-to-noise ratio SNR was larger than 2. Figure 12b shows the analysis of the spatial frequency of the system on the imaging plane, with more than $120\text{lines}∕\mathrm{mm}$ . Because the system has a zoom of 2.26, the object resolving power is then larger than $300\text{lines}∕\mathrm{mm}$ , which indicates that our developed digital imaging scanner has a high resolving power of about $3\mu \mathrm{m}$ .

Fig. 12

The sensitivity and resolving power of the developed digital imaging scanner.

3.1.

Identification of Bacteria by Gene Chips

The identification of bacteria using gene chips is an important parallel method capable of simultaneously detecting numerous different bacterial species in a single diagnostic test.

The surface of the glass chip was modified for covalent bonding to specific gene probes, and the chip was printed with four $6\times 6$ probe arrays by using the SmartArrayer™-48 (CapitalBio, Beijing, China), as shown in Fig. 13a . The array comprises one row of Escherichia coli probes for the chaperone Hsp70 gene, one row of the Xanthomonas campestris probes for the HtpG gene, one row of negative probes as quality report marks of the chip hybridization and three rows of positive probes used to demonstrate successful amplification. Normally, for the validation of results on the chip, the negative probes show a blank (or zero) signal, and the positive probes report a high fluorescent intensity signal. Conversely, if the negative probes are not blank (or have a high signal), or the positive probes report a low (or blank) signal, these indicate that either the chip is defective or that the experimental protocols have failed, and thus the experimental results will not be valid.

Fig. 13

Identification of E. coli and X. campestris.

The repetition of the same six probes in a row demonstrates the chip credibility and generates independent repeated signals for statistical analysis of the experiment. If E. coli were present in a sample, then the row of E. coli probes will show a high signal. Similarly, if there were X. campestris in a sample, the row of X. campestris probes will show a high signal, and if there are neither bacteria present, then their reporter probes will show a low (or zero) signal. The bacterial genes present in a sample are first amplified by PCR to produce fluorescently labeled DNA fragments that are complementary to the chip bound probes, and which can be selectively hybridized to them. As shown in Fig. 13, fluorescence signals detected by our developed digital imaging scanning system were compared to the signals detected by another commercial confocal scanner (Scanner Array 4000B). Figure 13b shows the detection results by using our developed digital imaging scanning system, and Fig. 13c are the results obtained using the Scanner Array 4000B confocal scanner. Both scanning images show the same identification results, with good specific and parallel outcomes. However, the different color processing of the scanning diagrams illustrates differences between our digital imaging scanning system and the Scanner Array 4000B confocal scanner, with our system generating higher quality images.

3.2.

Detection of Serum Antibodies by Protein Chips

The developed digital imaging scanning system is also useful for fluorescence detection of the immuno-reactions of proteins on chips. We describe here a protein microarray chip (surface modified with a gel for the covalent attachment of the antigen spots) for the parallel detection of autoantibodies in the serum of patients with several different autoimmune diseases. These include systemic supus erythmatosis (SLE), mixed connective tissue disease (MCTD), Sjögren’s syndrome (SS), systemic sclerosis (SSc), dermotomyositis (DM), and polymyositis (PM). The protein microarray chip was printed in a $7\times 6$ array of antigen probes using the CapitalBio SmartArrayer™-48 and the noncontact spray head. The array, as shown in Fig. 14a , includes two systemic quality controls (QC), a blank control (BC), a Sjögren’s syndrome B antigen (SSB), a reaction control (RC), a sclerosis $70\mathrm{kDa}$ (Scl) antigen probe, and a negative control (NC). Purified autoantigens (SSB, Scl) were also immobilized on the chip. The protein microarray chip was incubated with $30\mu \mathrm{L}$ of a mixture of the serum (diluted 1:100 with PBST) from two patients with different diseases (anti-SSB and anti-Scl), for $30\min$ at room temperature. After being rinsed and washed one time for $5\min$ with PBST, the chip was incubated with $30\mu \mathrm{L}$ of Cy3-labeled goat antihuman IgG antibody for $30\min$ at room temperature. After another rinse and several washes with PBST for $5\min$ , the chip was briefly centrifuged to dry it. The protein microarray chip was then scanned using our developed digital imaging scanning system in Fig. 14b, and the Scanner Array 4000B confocal scanner in Fig. 14c. The results of scanning images clearly showed that this mixed sera contained both anti-SSB and anti-Scl autoantibodies. Both systems gave the same autoantibody detection results; however, the differences in color processing of the scanning images by our developed digital imaging scanning system and the commercial confocal scanner are apparent, with our system generating higher quality images.

Fig. 14

Detection of patient serum autoantibodies by a protein chip.