Bilateral prediction and intersection calculation autofocus method for automated microscopy

Authors

  • Z.M. WU,

    1. Key Laboratory of Optoelectronic Technology and Systems of the Ministry of Education of China, Chongqing University, Chongqing, China
    2. Precision and Intelligence Laboratory, Department of Optoelectronic Engineering, Chongqing University, Chongqing, China
    Search for more papers by this author
  • D.H. WANG,

    1. Key Laboratory of Optoelectronic Technology and Systems of the Ministry of Education of China, Chongqing University, Chongqing, China
    2. Precision and Intelligence Laboratory, Department of Optoelectronic Engineering, Chongqing University, Chongqing, China
    Search for more papers by this author
  • F. ZHOU

    1. Key Laboratory of Optoelectronic Technology and Systems of the Ministry of Education of China, Chongqing University, Chongqing, China
    2. Precision and Intelligence Laboratory, Department of Optoelectronic Engineering, Chongqing University, Chongqing, China
    Search for more papers by this author

Dai-Hua Wang, Rm1404, Main Teaching Building, Chongqing University, Shaping ba, Chongqing 400044 China. Tel: +86 23 6511 2105; fax: +86 23 6511 2105; e-mail: dhwang@cqu.edu.cn

Summary

In this paper, a bilateral prediction and intersection calculation autofocus method for automated microscopy, which obtains the in-focus position by calculating the intersection of the predicted left and right focus measure curves located respectively in the left and right sides of the peak position of the focus measure curve, is proposed and performed. According to the autofocus method, the area including the peak position of the focus measure curve and its left and right neighbourhoods should be determined firstly, and the left and right neighbourhoods are considered as the left and right sampling areas. The left and right focus measure curves are predicted by appropriate predicting models according to the two sample sequences, which comprise the focus values by evaluating the sampled images in the left sampling area and right sampling area, respectively and their corresponding sampling positions. The intersection of the predicted left and right focus measure curves is calculated and can be considered as the in-focus position. The autofocus can be realized by moving the focus plane of the microscope to the intersection of the predicted left and right focus measure curves. The proposed bilateral prediction and intersection calculation autofocus method is experimentally verified in an automated light microscopy for implementing microassembly and micromanipulation. The theoretical analyses have shown that the proposed bilateral prediction and intersection calculation autofocus method can not only effectively avoid the principle error caused by assuming the symmetrical focus measure curve in the autofocus methods based on curve fitting, but also eliminate the possible waver search near the peak position in the modified fast climbing servo method. The experimental results have shown that the proposed bilateral prediction and intersection calculation autofocus method possesses the merits as follows: (1) the focusing accuracy is high and slightly affected by the sampling step size and (2) the focusing speed is higher than those of the 7-point hill-climbing search method and the quadratic curve fitting method with a determinate focusing accuracy.

Introduction

Automated microscopy has become an essential tool in human life and scientific research. The autofocus technology is one of the key technologies affecting the imaging quality and efficiency of automated microscopy. Generally, the autofocus technology can be categorized into the active autofocus method and the passive autofocus method (Sun et al., 2004). The autofocus systems applying the active autofocus method need additional optical paths and/or distance measuring equipments, which will increase the complexity and cost of automated microscopy. The passive autofocus method, which is based on image processing, does not need additional equipments (Loren, 2007) and is beneficial to the integration and miniaturization of automated microscopy. Therefore, the autofocus method based on image processing has been widely researched and applied in automated microscopy.

The autofocus technology based on image processing should solve two relative problems: (1) the focus measure for evaluating image pixel information (Yeo et al., 1993; Geusebroek et al., 2000; Sun et al., 2004; Bueno-Ibarra et al., 2005; Loren, 2007; Lee et al., 2008; Lee et al., 2009; Koh et al., 2011; Tian, 2011; Liang & Qu, 2012) and (2) the autofocus method for searching in-focus position (Ooi et al., 1990; Baina & Dublet, 1995; Choi et al., 1999; He et al., 2003; Kehtarnavaz & Oh, 2003; Chen et al., 2006; Oku & Ishikawa, 2006; Yazadanfar et al., 2008; Brazdilova & Kozubek, 2009; Pengo et al., 2009; Yoon & Park, 2009). Up to now, there are many research works on the focus measures. However, because of the unforeseen property of the autofocus process, the research works on the autofocus methods are relatively less. In the existing autofocus methods, the mountain climbing servo or the hill-climbing search (HCS) method, which might be the first search method for autofocus, has been widely used to construct the autofocus systems for cameras and automated microscopy (Ooi et al., 1990). The major problems of the HCS method lie in the slow convergence speed of autofocus and the high probability of defocus. To speed up the autofocus of digital cameras, He et al. (He et al., 2003) developed a modified fast climbing servo method by dynamically altering the focus step size according to the difference between the current focus value and the previous focus value in a focus process. Yoon and Park (Yoon & Park, 2009) realized the HCS method with the difference between the maximum value and the minimum value and two-stage search method and the impulsive noise can be reduced without additional filter. To reduce the computation in the autofocus based on the HCS method, different sampling strategies, such as the subsampling method, the subwindow method (Choi et al., 1999) and the Halton sampling method (Pengo et al., 2009) and different focus measures are adopted.

Except the HCS method, the binary search method and the Fibonacci search method (Baina & Dublet, 1995), which are two other simple autofocus methods, have been proposed for quick searching. However, the binary search method and the Fibonacci search method not only are easily affected by noise, but also cause long movement distance and fro movement of lens. Dividing the focus range into four types of search areas, including the initial, fine, mid and coarse, Kehtarnavaz and Oh (Kehtarnavaz & Oh, 2003) presented a rule-based autofocus method for digital cameras to reduce the number of focus iterations and power consumption. Chen et al. (Chen et al., 2006) proposed and studied a real-time autofocus method by searching the in-focus position with the discrete difference equation predicting model during the coarse search procedure and with the bisection search method during the fine search procedure.

To observe cells and biological tissues, Oku and Ishikawa (Oku & Ishikawa, 2006) proposed a depth from diffraction method to estimate the depth from only single defocused image within 1 ms using a high-speed image processing system. Yazadanfar et al. (Yazadanfar et al., 2008) proposed an autofocus method by combining Brenner gradient and curve fitting to calculate the in-focus position with no more than three images. Brazdilova and Kozubek (Brazdilova & Kozubek, 2009) divided focus measure curve into the mild and steep regions according to the absolute derivatives and proposed an adaptive autofocus algorithm for multimodal focus measure curve.

In the existing autofocus methods, the in-focus positions are mostly determined by comparing the difference between the current focus value and the previous focus value. On one hand, when the sampling step size is small, some methods are inefficient and easily fail because of the local peaks. On the other hand, when the sampling step size is large, the focusing accuracy of some methods is low. Even the modified fast climbing servo method is fast for autofocus, it just uses the difference of two focus values to set the adaptive step size, which may lead a waver search near the peak position. The autofocus methods based on curve fitting will introduce the principle error by assuming the actual asymmetrical focus measure curve as symmetrical about the peak position of the focus measure curve.

In this study, a bilateral prediction and intersection calculation (BPIC) autofocus method for automated microscopy is proposed and realized. In an automated light microscopy for implementing the microassembly and micromanipulation, the proposed BPIC autofocus method is experimentally verified.

BPIC autofocus method

Operation principle

The autofocus methods based on image processing mainly rely on the features of the focus measure curve. Figure 1 shows the common variance focus measure curve for characterizing a focus process. In Figure 1, sp represents the peak position of the focus measure curve and sl and sr represent the leftmost and rightmost positions of the neighbourhood of the peak position of the focus measure curve, respectively. The left and right neighbourhoods of the peak position of the focus measure curve can be expressed as inline image and inline image, respectively. Hence, the left and right focus measure curves [fl(s) and fr(s)] in the left and right neighbourhoods can be expressed as

image(1)

where FV(s) is the focus value of the sampled image at the sampling position of s.

Figure 1.

Variance focus measure curve.

According to Figure 1 and Eq. (1), the peak position of the focus measure curve can be seen as the intersection of the left and right focus measure curves fl(s) and fr(s). In response to the aforementioned feature of the focus measure curve, a BPIC autofocus method for automated microscopy is proposed. According to the proposed BPIC autofocus method, the area including the peak position of the focus measure curve and its left and right neighbourhoods should be determined, and the left and right neighbourhoods are considered as the left sampling area (LSA) and right sampling area (RSA), respectively. The left and right focus measure curves in the left and right sides of the peak position are predicted by appropriate predicting models using the two sample sequences, which are composed of the focus values by evaluating the sampled images in the LSA and RSA, respectively and their corresponding sampling positions. The intersection of the predicted left and right focus measure curves is calculated and the autofocus can be realized by moving the focus plane of the microscope to the intersection. Figure 2 illustrates the operation principle of the proposed BPIC autofocus method.

Figure 2.

Schematic of the BPIC autofocus method: (a) determining the LSA and RSA, (b) sampling and predicting in the LSA, (c) sampling and predicting in the RSA and (d) determining the intersection of the predicted left and right focus measure curves.

Firstly, as shown in Figure 2(a), the area including the peak position of the focus measure curve, inline image, and the left and right neighbourhoods of the area, inline image and inline image, are determined by appropriate ways. inline image and inline image are considered as the LSA and RSA, respectively. Secondly, as shown in Figures 2(b) and (c), the two sample sequences, Sl and Sr, are obtained by evaluating the images sampled in the LSA and RSA with certain sampling step size. The two sample sequences can be expressed as

image(2)
image(3)

where n and m are the number of the samples of Sl and Sr, respectively; inline image and inline image are the ith samples of Sl and Sr, respectively; inline image and m for Sl and Sr, respectively; sl(i) and FVl(i) are the ith sampling position and the corresponding focus value of Sl, respectively; sr(i) and FVr(i) are the ith sampling position and the corresponding focus value of Sr, respectively; N* is a positive integer.

Considering the prediction model as

image(4)

where f(s) and inline image represent the prediction model and the predicting result, respectively. The predicting result inline image is the predicted focus measure curve. Considering inline image and inline image are the predicted left and right focus measure curves according to Eq. (4), the intersection of the predicted left and right focus measure curves, as shown in Figure 2(d), can satisfy

image(5)

The intersection inline image given by Eq. (5) is not only the predicted peak position of the focus measure curve but also the in-focus position of the microscope. The autofocus is performed by moving the focus plane of the microscope to the intersection given by Eq. (5).

Because of the independent prediction for the left and right focus measure curves, the proposed BPIC autofocus method can be used without assuming the actual asymmetrical focus measure curve as symmetrical about the peak position of the focus measure curve. Therefore, the proposed BPIC autofocus method can avoid the principle error caused by assuming the actual asymmetrical focus measure as symmetrical one about the peak position in the autofocus method based on curve fitting. Because the in-focus position is the intersection of the predicted left and right focus measure curves, the proposed BPIC autofocus method can obtain the in-focus position without letting the microscope pass repeatedly the peak position of the focus measure curve, so that the proposed BPIC autofocus method can eliminate the possible waver search near the peak position in the modified fast climbing servo method.

The sampling step sizes in the LSA and RSA, the number of the samples included in the left and right sample sequences and the bilateral prediction models may be different during the implementation of the proposed BPIC autofocus method. To implement the proposed BPIC autofocus method, the variance function is taken as the focus measure, the 7-point HCS method is used to determine the area including the peak position of the focus measure curve and the corresponding LSA and RSA and the exponential prediction model is used to predict the trends of the left and right focus measure curves.

Variance focus measure

The variance focus measure is expressed as (Yeo et al., 1993)

image(6)

where h and w represent the numbers of the pixels in the width and height of an image, respectively; i(x, y) represents the pixel grey value of the image at coordinate (x, y); inline image represents the mean of all pixel grey values in the image.

LSA and RSA

Using the 7-point HCS method, the peak of the focus measure curve can be expressed as

image(7)

According to Eq. (7), s(4), which is the sampling position of FV (4), is the peak position of the focus measure curve. Hence, the area including the peak position of the focus measure curve can be expressed as

image(8)

According to Eqs (7) and (8), the LSA and RSA can be given by inline image and inline image, respectively. In practice, the two sequences of inline image and inline image obtained by the 7-point HCS method are usually regarded as the left and right sample sequences.

Exponential prediction model

We have empirically observed that the unilateral trend of the variance focus measure curve can be imitated by the exponential prediction model (Fu & Liu, 2003). Applying the exponential prediction model, Eq. (4) can be rewritten as

image(9)

where a and b are the model parameters and s is the sampling position.

To utilize the least-squares method to determine the model parameters a and b, Eq. (9) can be expressed as

image(10)

Substituting one sample sequence into Eq. (10) yields

image(11)

Utilizing the least-squares method, the solution of Eq. (11) can be expressed as

image(12)
image

Substituting the left and right sample sequences give by Eqs (2) and (3) into Eq. (12) yields the model parameters, inline image and inline image, of the bilaterally exponential prediction model. Substituting the model parameters into Eq. (10) yields the predicted left and right focus measure curves as follows

image(13)

According to Eq. (13), the intersection of the predicted left and right focus measure curves is determined by

image(14)

The autofocus is implemented by moving the focus plane of the microscope to the intersection given by Eq. (14).

Process of the BPIC autofocus method

Considering the variance function as the focus measure, employing the 7-point HCS method to determine the LSA and RSA and utilizing the exponential prediction model as the bilateral prediction models, the implement of the proposed BPIC autofocus method includes the steps as follows

  • Step 1. Determine the correct focus direction according to the focus direction judgement method based on threshold (Wang et al., 2010) and obtain seven samples by the 7-point HCS method and the variance focus measure.

  • Step 2. Judge whether the maximum focus value in the latest seven samples comes from the first, second or third sample. If yes, reverse the order of the latest seven samples and the focus direction, save the reversed samples and the reversed focus direction as the latest samples and the correct focus direction and increase one sample in the next sampling position of the reversed seventh sample according to the reversed focus direction, then repeat Step 2. If no, judge whether the maximum focus value locates at the 4th sample of the latest seven samples by Eq. (7). If no, increase one sample according to the focus direction, and repeat Step 2; if yes, continue the next step.

  • Step 3. Take the latest sequences of inline image and inline image as the left and right sample sequences, respectively.

  • Step 4. Obtain the model parameters, inline image and inline image, of the bilaterally exponential prediction model by solving Eq. (12) in least-squares sense.

  • Step 5. Calculate the intersection of the predicted left and right focus measure curves by Eq. (14), and implement the autofocus by moving the focus plane of the microscope to the intersection.

Experimental results and analysis

Experimental set-up

The schematic and photograph of the established experimental set-up are shown in Figures 3(a) and (b), respectively. In Figure 3, the experimental set-up consists of a 12× zoom microscope (Navitar, Rochester, NY, USA) with a LED light source (Ti-Times, ShenZhen, GuangDong, China), a TM-1325CL CCD camera (JAI, Yokohama, Kanagawa, Japan), a X64CL-Express frame grabber (Dalsa, Quebec, Canada), a motorized translation stage with motion controller (Winner Optics, Beijing, China) and a host computer (2.50 GHz×2 CPU and 2.0 GB RAM). The resolution of the motorized translation stage is 0.13 μm. Utilizing the established experimental set-up, the focusing accuracy and the focusing speed of the BPIC autofocus method are tested and compared with those of the 7-point HCS method and the quadratic curve fitting (QCF) method (Iannello et al., 2011).

Figure 3.

Experimental set-up: (a) the schematic and (b) the photograph.

Initial sampling positions (ISPs)

When doing experiments, the autofocus individually starts from inline image different ISPs and the peak positions of the focus measure curve are predicted or searched, respectively. The first ISP is the origin of the motorized translation stage and set automatically by the motorized translation stage. The jth ISP is determined by moving a distance dj from the first ISP along the focus direction. The distance dj can be expressed as

image(15)

where j (j= 1, 2, … , t) is the ordinal number of the ISP, t is the total number of the ISPs and L is the sampling step size.

Focusing accuracy

The focusing accuracy is characterized by the in-focus position error (IFPE), which is defined by the absolute difference between the predicted or searched peak position and the actual peak position of the focus measure curve. In experiments, the focusing accuracy of the BPIC autofocus method, the 7-point HCS method and the QCF method have been tested individually and compared with different sampling step sizes and different microscope objectives. The total number (t) of the ISPs is set as 10 in the two cases.

(1) Autofocus with different sampling step sizes.

The peak positions of the focus measure curve predicted by the BPIC autofocus method, searched by the 7-point HCS method and predicted by the QCF method with sampling step sizes of 0.026, 0.078 and 0.65 mm are shown in Table 1 when a microscope objective of 2.5× is used and the actual peak position is 8.047 mm away from the origin of the motorized translation stage. According to Table 1, the relationships between the IFPEs and the ISPs (represented by the ordinal number of the ISP) by the three methods with different sampling step sizes are shown in Figures 4(a), (b) and (c), respectively.

Table 1.  Peak positions predicted by the BPIC autofocus method, searched by the 7-point HCS method and predicted by the QCF method with different sampling step sizes.
ISPPeak position (mm)
L= 0.026 mm L= 0.078 mm L= 0.65 mm
BPIC7-point HCSQCFBPIC7-point HCSQCFBPIC7-point HCSQCF
08.036088.03408.054028.045058.068.065858.064557.88.03075
0.1L8.059748.06268.053118.041158.06788.064558.060917.8657.98811
0.2L8.040508.03928.053898.043888.07568.052078.04447.937.98785
0.3L8.042718.04188.054548.045188.08348.071448.045967.9958.0197
0.4L8.045058.04448.059618.048438.09128.06398.044798.068.06325
0.5L8.044278.04708.051948.059098.0218.055198.04188.1258.11057
0.6L8.048828.04968.056758.054548.02888.060788.026338.198.1523
0.7L8.051558.05228.051168.051298.03668.048698.037648.2558.18402
0.8L8.053248.05488.054028.048178.04448.068978.025688.328.16231
0.9L8.054288.05748.057148.046748.05228.064298.055067.7358.14385
Figure 4.

Relationships between the IFPEs and the ISPs (represented by the ordinal number of the ISP) when the sampling step size is: (a) 0.026 mm, (b) 0.078 mm and (c) 0.65 mm.

In Figure 4(a), the sampling step size for three autofocus methods is set as 0.026 mm, the IFPEs by the BPIC autofocus method are less than those by the 7-point HCS method except in the sixth ISP and the IFPEs by the BPIC autofocus method and the QCF method are interlaced. Both the maximum IFPE of 0.01274 mm by the BPIC autofocus method and the maximum IFPE of 0.0156 mm by the 7-point HCS method occur in the second ISP, the maximum IFPE of 0.01261 mm by the QCF method occurs in the fifth ISP. In Figure 4(b), the sampling step size for three autofocus methods is set as 0.078 mm, the IFPEs by the BPIC autofocus method are less than those by the 7-point HCS method and those by the QCF method except in the sixth and eighth ISPs. The maximum IFPEs of 0.01209 mm by the BPIC autofocus method occurs in the sixth ISP, the maximum IFPEs of 0.0442 mm by the 7-point HCS method occurs in the fifth ISP and the maximum IFPEs of 0.02444 mm by the QCF method occurs in the fifth ISP. The maximum IFPE by the BPIC autofocus method is 27.35% of that by the 7-point HCS method and 50% of that by the QCF method. In Figure 4(c), the sampling step size for three autofocus methods is set as 0.65 mm, the IFPEs by the BPIC autofocus method are less than those by both the 7-point HCS method and the QCF method. The maximum IFPEs of 0.02132 mm by the BPIC autofocus method occurs in the ninth ISP, the maximum IFPEs of 0.312 mm by the 7-point HCS method occurs in the tenth ISP and the maximum IFPEs of 0.13702 mm by the QCF method occurs in the eighth ISP. The maximum IFPE by the BPIC autofocus method is 6.8% of that by the 7-point HCS method and 15.6% of that by the QCF method.

According to the above analysis, when the sampling step size increases 24 times from 0.026 to 0.65 mm, the maximum IFPEs by the BPIC autofocus method increase less than one time from 0.01274 to 0.02132 mm and the maximum IFPEs by the 7-point HCS method and the QCF method increase 19 times from 0.0156 to 0.312 mm and 10 times from 0.01261 to 0.13702 mm, respectively. The phenomenon may be attributed to that the fitting errors by the asymmetric focus measure curve are increased with increasing the sampling step size over the wider sampling area. The experimental results indicate that the focusing accuracy of the BPIC autofocus method is slightly affected by the sampling step size, the focusing accuracy of the QCF method is moderately affected by the sampling step size and the maximum IFPE by the 7-point HCS method approximately equals the half of the sampling step sizes used in the corresponding experiments. In summary, in light of the focusing accuracy, the BPIC autofocus method is superior to both the 7-point HCS method and the QCF method with increasing the sampling step size under the fixed microscope objective.

Figure 5 shows the in-focus images of the number '8' with size of two pounds from the ninth ISP with the BPIC autofocus method, the tenth ISP with the 7-point HCS method and the eighth ISP with the QCF method when the microscope objective is 2.5× and the sampling step size is 0.65 mm. Every image in Figure 5 is the one with the worst IFPE among the 10 in-focus images by the corresponding autofocus methods. As shown in Figure 5, the image of the number '8' by the BPIC autofocus method is very clear, the image of the number '8' by the 7-point HCS method is blurry, whereas the clarity of the image of the number '8' by the QCF method is between Figures 5(a) and (b).

Figure 5.

In-focus images of the number '8' by (a) the BPIC autofocus method, (b) the 7-point HCS method and (c) the QCF method.

(2) Autofocus with different microscope objectives.

The peak positions of the focus measure curve predicted by the BPIC autofocus method, searched by the 7-point HCS method and predicted by the QCF method with the microscope objectives of 1.5×, 2.5× and 3.5× are shown in Table 2 when the sampling step size is 0.078 mm. The actual peak positions are 7.982, 8.047 and 8.0444 mm away from the origin of the motorized translation stage for the three magnifications of the microscope objectives, respectively. According to the actual peak positions and Table 2, the relationships between the IFPEs and the ISPs (represented by the ordinal number of the ISP) by the three methods with the microscope objectives of 1.5×, 2.5× and 3.5× are shown in Figures 6(a), (b) and (c), respectively.

Table 2.  Peak positions predicted by the BPIC autofocus method, searched by the 7-point HCS method and predicted by the QCF method with different microscope objectives.
ISPPeak position (mm)
Microscope objective of 1.5×Microscope objective of 2.5×Microscope objective of 3.5×
BPIC7-point HCSQCFBPIC7-point HCSQCFBPIC7-point HCSQCF
07.980577.9828.008138.045058.068.065858.034918.068.06039
0.1L7.983047.98987.988638.041158.06788.064558.034268.06788.06468
0.2L7.991627.99768.003068.043888.07568.052078.033098.07568.04739
0.3L7.997218.00548.010998.045188.08348.071448.032578.08348.06663
0.4L7.999558.01327.992798.048438.09128.06398.05748.01328.04830
0.5L8.005018.0217.998908.059098.0218.055198.055848.0218.05857
0.6L7.958477.95087.995398.054548.02888.060788.053378.02888.05896
0.7L7.966147.95867.986948.051298.03668.048698.05228.03668.05909
0.8L7.967447.96648.010348.048178.04448.068978.046098.04448.06221
0.9L7.969917.97428.002028.046748.05228.064298.04448.05228.05493
Figure 6.

Relationships between the IFPEs and the ISPs (represented by the ordinal number of the ISP) with the microscope objectives of: (a) 1.5×, (b) 2.5× and (c) 3.5×.

In Figure 6(a), the microscope objective for three autofocus methods is set as 1.5×, the IFPEs by the BPIC autofocus method are less than those by the 7-point HCS method except in the first and tenth ISPs and the IFPEs by the BPIC autofocus method and the QCF method are interlaced. The maximum IFPEs of 0.02353 mm by the BPIC autofocus method occurs in the seventh ISP, the maximum IFPEs of 0.039 mm by the 7-point HCS method occurs in the sixth ISP, the maximum IFPEs of 0.02899 mm by the QCF method occurs in the fourth ISP. Figure 6(b) is obtained with the microscope objective of 2.5× and the sampling step size of 0.078 mm and the description can be referred to that of Figure 4(b). In Figure 6(c), the microscope objective for three autofocus methods is set as 3.5×, the IFPEs by the BPIC autofocus method are less than those by the 7-point HCS method except in the ninth ISP and those by the QCF method except in the third and fifth ISPs. The maximum IFPE of 0.013 mm by the BPIC autofocus method occurs in the fifth ISP, both the maximum IFPE of 0.039 mm by the 7-point HCS method and the maximum IFPE of 0.02223 mm by the QCF method occur in the fourth ISP.

As analysed above, the maximum IFPEs by the BPIC autofocus method are limited in a small range, the maximum IFPEs by the 7-point HCS method approximately equal the half of the sampling step sizes used in the corresponding experiments and the maximum IFPEs by the QCF method are between the maximum IFPEs by the BPIC autofocus method and by the 7-point HCS method. The conclusion can be drawn that the BPIC autofocus method has high focusing accuracy, the focusing accuracy of the 7-point HCS method mainly relies on the sampling step size and the focusing accuracy of the QCF method is inferior to that of the BPIC autofocus method and superior to that of the 7-point HCS method under different microscope objectives.

Focusing speed

Figure 4 indicates that the maximum IFPEs by the BPIC autofocus method, the 7-point HCS method and the QCF method slightly, drastically and proportionally and moderately increase with increasing the sampling step size, respectively. Figure 7 shows the relationships between the IFPEs and the ISPs (represented by the ordinal number of the ISP) by the BPIC autofocus method with the sampling step size of 0.078 mm and the 7-point HCS method and the QCF method with the sampling step size of 0.026 mm, using the microscope objective of 2.5×. As shown in Figure 7, when other experimental conditions are same and the sampling step size of the BPIC autofocus method is three times of that of the 7-point HCS method and the QCF method, the maximum IFPE by the BPIC autofocus method is less than that by the 7-point HCS method and the QCF method. That is to say, when the sampling step size used in the BPIC autofocus method is larger than that used in the 7-point HCS method and the QCF method in practical applications, the focusing accuracy of the BPIC autofocus method is still higher than that of the 7-point HCS method and the QCF method. During the autofocus, the focusing speed strongly relies on the total number of the sampled images for implementing the autofocus. The larger the sampling step size is, the less the total number of the sampled images for implementing the focus is and the faster the focusing speed is. In this case, we can conclude that the focusing speed of the BPIC autofocus method is higher than those of the 7-point HCS method and the QCF method.

Figure 7.

Relationships between the IFPEs and the ISPs (represented by the ordinal number of the ISP).

Conclusions

This paper has reported the BPIC autofocus method for performing the autofocus of automated microscopy quickly and accurately. In the automated light microscopy for implementing the microassembly and micromanipulation, the BPIC autofocus method was realized. In the autofocus process with the BPIC autofocus method, the area including the peak position of the focus measure curve and its left and right neighbourhoods were determined by the 7-point HCS method firstly and the left and right neighbourhoods were considered as the LSA and RSA, respectively. The left and right focus measure curves were predicted by the exponential predicting model according to the two sample sequences, which were comprised of the focus values by evaluating the sampled images in the LSA and RSA, respectively with the variance function and their corresponding sampling positions. The intersection of the predicted left and right focus measure curves was calculated and was considered as the in-focus position. The autofocus was realized by moving the focus plane of the automated light microscope to the intersection of the predicted left and right focus measure curves. The theoretical analyses have shown that the proposed BPIC autofocus method can not only effectively avoid the principle error caused by assuming the symmetrical focus measure curve in the autofocus methods based on curve fitting, but also eliminate the possible waver search near the peak position in the modified fast climbing servo method. The experimental results have shown that the proposed BPIC autofocus method possesses the merits as follows: (1) the focusing accuracy is high and slightly affected by the sampling step size and (2) the focusing speed is higher than those of the 7-point HCS method and the QCF method with a determinate focusing accuracy.

It is worth noting that the sampling step sizes in the LSA and RSA, the number of the samples included in the left and right sample sequences and the bilateral prediction models may be different during the implementation of the proposed BPIC autofocus method.

Ancillary