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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

We overview an approach to providing automated three-dimensional (3D) sensing and recognition of biological micro/nanoorganisms integrating Gabor digital holographic microscopy and statistical sampling methods. For 3D data acquisition of biological specimens, a coherent beam propagates through the specimen and its transversely and longitudinally magnified diffraction pattern observed by the microscope objective is optically recorded with an image sensor array interfaced with a computer. 3D visualization of the biological specimen from the magnified diffraction pattern is accomplished by using the computational Fresnel propagation algorithm. For 3D recognition of the biological specimen, a watershed image segmentation algorithm is applied to automatically remove the unnecessary background parts in the reconstructed holographic image. Statistical estimation and inference algorithms are developed to the automatically segmented holographic image. Overviews of preliminary experimental results illustrate how the holographic image reconstructed from the Gabor digital hologram of biological specimen contains important information for microbial recognition.

Optical imaging systems using digital holography under coherent illumination have been studied in three-dimensional (3D) display, medical diagnosis, 3D microscopy, robotics, defense, and security [

Recently, information photonics-based optical sensing/imaging systems have been investigated for continuous, automated detection and identification of biological specimens [

Most conventional methods used to inspect and identify biological specimens typically involve time-consuming and labor-intensive biochemical assays or imaging and digital processing. Many imaging methods identify microorganisms based on specific two-dimensional (2D) shape information, image intensity color profile, and/or aggregation size and reaction time. However, a number of specimens such as protozoan cell structures, bacteria, and sperm tails are essentially fully transparent unless stained. This staining process is invasive for biological cells so that their viability can be adversely affected, which can be undesirable for certain studies of biological specimens. In addition, imaging methods often fail to recognize very minute differences in thickness, size, and shape. To overcome these obstacles, interferometry-based bio-sensing/imaging techniques have been developed to study biological specimens. In these techniques, the phase of a passing coherent light beam is changed by the differing densities and compositions within a biological specimen. Phase information can be recorded interferometrically, allowing for the study of biological specimens that would otherwise die from staining or be invisible to conventional imaging means. Here, optical sensing/imaging system integrated with information photonics for rapid, reliable sensing and identification of biological specimens is reviewed. This paper is an overview of the work we have done in real time identification of micro/nanoorganisms using 3D computational holographic imaging [

The Gabor digital holographic microscopy [

For the phase information acquisition of biological specimens, the magnified diffraction patterns of biological specimens are optically recorded by the presented Gabor digital holographic microscopy interfaced with a computer. Next, the magnified 3D image or stack of 2D images of a biological specimen is numerically reconstructed from the Gabor digital hologram by using the Huygens-Fresnel principle integral [

For the automatic identification of biological specimens, the segmented areas of the reconstructed holographic images are used for selection of random test pixels used to build up the test statistic for recognition. It is more efficient to first filter out the unnecessary background from computationally reconstructed holographic images before feeding them into recognition modules. The segmentation helps finding regions of interest before processing for recognition. In this overview paper, the watershed image segmentation algorithm [

These statistical sampling techniques allow for fast microbial identification and are found to be much more suitable in identifying the minute and morphologically simple species that are similar in their thickness, size and/or shape. Also, statistical hypothesis testing with the statistical sampling datasets can be applied to distinguish between different classes of biological microorganisms. These samples are processed using statistical inference algorithms for the equality of dispersions between the sampling segments of the reference and unknown input class holographic images. Statistical parametric and nonparametric estimators [

The interferometery-based microscope discussed in this overview paper enables thickness measurements to be made that are not subject to these particular limitations, because with this technique the phase-change in the wavefront modulated by the specimen can be measured very accurately. Therefore the phase information for the specimens, which depends on the refractive index distribution of cellular cytoplasmic content and thickness of the specimen, can be measured in digital holographic microscopy. We believe, as our experiments show repeatedly, that biological organisms have their own unique characteristic phase distributions that can be exploited for their automatic identification.

Gabor digital holographic microscopy [

After recording the Gabor digital hologram, a number of methods can be used for computational reconstruction of original bio-specimens including convolution and angular spectrum approaches [

Let the field distribution of a biological specimen

The interference pattern or Gabor digital hologram recorded at the CCD plane or hologram plane is represented as follows:
_{h}_{r}_{0}_{x}_{y}

In the following, the design procedure to evaluate the microbial identification performance of the 3D sensing system based on Gabor digital holographic microscopy is described. For the automatic identification of bio-specimens, the segmented areas of the reconstructed holographic images are used for selection of random test pixels used to build up the test statistic for recognition. It is more efficient to first filter out the unnecessary background from computationally reconstructed holographic images before feeding them into recognition modules. The segmentation helps finding regions of interest before processing for recognition. In this overview paper, the watershed image segmentation algorithm has been used to efficiently remove the background part of the reconstructed image on the computer. Then, we randomly extract

These statistical sampling methods allow for fast microbial identification and are found to be much more suitable in identifying the minute and morphologically simple species that are similar in their thickness, size and/or shape. Also, statistical hypothesis testing with the statistical sampling datasets can be applied to distinguish between different classes of biological microorganisms.

Our purpose of this overview paper is to illustrate that the digital holographic image or complex signal modulated by the specimen contains a rich data set for quantitative characterization and recognition of bio-specimens by using the statistical sampling methods and statistical hypothesis testing. Meanwhile, the advanced image recognition algorithms can be developed in order to improve the microbial identification performance. The statistical methodology for identification of biological specimens using digital holographic images is described in

From the histogram analysis of the real and imaginary parts of the digital holographic image, it is assumed that the random variables (real or imaginary parts of the segmented holographic image) in the sampling segment nearly follow Gaussian distribution [

The statistical sampling distributions for the difference of parameters between the sample segment features of the reference and unknown input class digital holographic images can be calculated by using statistical estimation algorithms. The parametric statistical methods [

For comparing dispersion parameters, the sampling distribution of the ratio between two sample variances is computed. It is assumed that random variables

For comparing the dispersion parameters between two sampling segments, we assume that all four statistical parameters are unknown and
_{r}_{i}_{r}_{i}_{0}_{1}_{0}

On the basis of a two-tailed test at a level of significance

Accept _{0}_{(nr−1), (ni−1),α/2} to _{(nr−1), (ni−1), 1−α/2}.

Reject _{0}

The upper 100 × (_{(nr−1), (ns−1)} distribution denotes _{(nr−1), (ns−1),α/2}. This decision rule implies that _{0}_{α/2}and _{1−α/2} given the probability density function of the _{α2/2} and _{1−α2/2}. Thus the following probability can be claimed [

Finally, the statistical p-value is computed by empirical Monte Carlo techniques for the statistical decision to classify the specimen. It is a common practice to reject the null hypothesis if the calculated statistical p-value is less than 0.05. However, other cut-off p-values are also applicable, for example 0.01 or 0.10.

In the following, a statistical distribution-free test (KS-test) [^{r}^{r}^{r}^{r}^{r}^{r}^{i}^{r}^{i}

In the following, the 3D visualization of micro/nano biological organisms using Gabor digital holographic microscopy is presented. In the experiments biological specimens were around several μm in size. Their Gabor digital holograms were recorded with a CCD array of 2,048 × 2,048 pixels and a pixel size of 9 μm × 9 μm, where the biological specimen was sandwiched between two transparent cover slips.

For preliminary evaluation of the recognition performance, a hypothesis testing [null hypothesis:

For preliminary evaluation of the recognition performance, a hypothesis testing [null hypothesis:

Automated micro/nano biological organism sensing and recognition system using Gabor digital holographic microscopy and a statistical inference has been overviewed. 3D sensing is based on Gabor digital holographic microscopy. In order to evaluate the recognition performance of the presented microbial sensing system, the Gabor digital holograms of biological specimens have been optically measured and then the complex holographic images of the original biological specimens have been digitally reconstructed with the recorded Gabor digital hologram. Target sampling segments have been extracted in the segmented holographic image after applying watershed image segmentation algorithm to the reconstructed holographic image. The sampling probability distribution of the difference of the ratio of the dispersions have been calculated between the reference and unknown input class sampling segments varying the sample size of sampling segment. Finally, the presented sensing system has been tested by performing hypothesis tests for the difference of the ratio of variances with a statistical decision rules. It has been shown in preliminary experiments that the holographic image reconstructed from only a single Gabor digital hologram of biological specimen contains important information for recognition and classification and they may be identified using a statistical estimation and inference algorithms. The shapes of some bacteria and algae are filamentous, spherical, and branched. They may look similar in terms of shape. This approach allows the presented system to be tolerant of shape in recognizing biological specimens like bacteria or algae.

This research was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0088195). This research was supported in part by the Korea Research Foundation Grant funded by the Korean Government (KRF-2010-L030102-06B2005)

Experimental setup for recording the Gabor digital hologram of bio-specimens.

Statistical methodology to implement the presented three-dimensional microbial sensing/recognition system [

The microbial holographic images reconstructed at the distance 25μm from their Gabor digital holograms and binary windows for targets obtained by using a watershed image segmentation algorithm.

Parametric F-test results for the equality of two variances. 200 test pixel points were selected from segmented holographic image.

The average statistical p-value calculated from the parametric F-test.

Nonparametric KS-test results for the equality of two variances. 200 test pixel points were selected from segmented holographic image.

The average statistical p-value calculated from the nonparametric KS-test.

The ROC-curve results between reference and false class statistical distributions. The distributions are generated from the test statistic F-test and KS-test. Sampling segments are obtained from both real and imaginary parts in the reconstructed complex image.