An approach for sensing marine plankton using digital holographic imaging

Optik 124 (2013) 6611–6614

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Optik journal homepage: www.elsevier.de/ijleo

An approach for sensing marine plankton using digital holographic imaging Shizhe Tan ∗ , Shengxu Wang Department of Electronic Engineering, Ocean University of China, Qingdao 266071, Shandong, China

a r t i c l e

i n f o

Article history: Received 25 December 2012 Accepted 18 May 2013

Keywords: Digital holographic imaging Marine plankton Numerical reconstruction

a b s t r a c t The goal of this paper is to use digital holographic imaging for sensing marine plankton in recording sampling volume. The process stage of this approach includes: wavefront recording using in-line holographic recording set up and numerical reconstruction using Fresnel approximation and convolution algorithm. So, by capturing hologram of marine plankton and reconstructing hologram, the recorded optical field of marine plankton is retrieved. Digital holographic imaging is an extremely powerful technique for the study of marine plankton fields as it allows instantaneous, noninvasive, high-resolution recording of substantial volumes. Finally, this paper presents that it is possible for digital holographic imaging system to sense marine plankton according to laboratory results. © 2013 Elsevier GmbH. All rights reserved.

1. Introduce Marine plankton, such as copepod, plays a key role in biological oceanography system. Many research efforts are played in sensing marine plankton. Digital holographic imaging is an extremely powerful technique for the study of marine plankton fields as it allows instantaneous, noninvasive, high-resolution recording of substantial volumes. Holography, invented by D Gabor in 1948, is a two-step imaging technique based on the principle of optics interference and diffraction. Because hologram can record not only the amplitude but also the phase information of object wave simultaneously, and the three-dimensional image of the object is obtained through reconstructed hologram. So, holography, a main metrological technique, has been applied in optical metrology. Due to its potential advantages, attempts to use holography for marine plankton detection started during the late 1960s and early 1970s, initially in laboratory studies [1–6]. Katz et al. [7] and O’Hern et al. [8] developed the first submersible, pulsed ruby-laser-based holography system and used it to measure the number and sizes of particles and bubbles in waters off Catalina Island. Watson et al. [9], Foster and Watson [10] and Hobson et al. [11] used hologrammetry to study the distribution of plankton in water-filled observation tanks. Nebrensky et al. [12] developed a submersible holographic camera for measuring the particle distributions, characteristics and motions within

∗ Corresponding author at: Department of Electronic Engineering, Ocean University of China, Songling Road 238,Qingdao 266071, Shandong Province, China. Tel.: +86 13853226600; fax: +86 0532 66782339. E-mail address: [email protected] (S. Tan). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.05.025

a sample volume in the ocean. More recently, groups led by Katz et al. [13], Craig et al. [14] and Watson et al. [15] have further developed and refined subsea ‘holocameras’. Watson’s camera (HoloMar system) was built around a frequency-doubled Nd-YAG laser and designed to record simultaneous in-line and off-axis holograms. With the development of high-resolution CCD, digital holography have used for a wide range of biological applications. The first reported use of digital holography for plankton studies was by Owen and Zozulya [16]. Since then, a number of researchers such as Xu et al. [17], Watson et al. [18] and Sun et al. [19–21] have used this technique. In this paper, we firstly discuss basic principles of digital holographic imaging for understanding our work, and then we design a digital holographic imaging experiment system for obtaining hologram of marine plankton. Finally, we discussed numerical reconstruction algorithm for obtaining image of marine plankton. 2. Basic principles of digital holographic imaging In digital holographic imaging, the hologram is recorded in a charge-coupled device (CCD), and the object is reconstructed using numerical methods. In the following section, the basic principles and formulations of digital holographic imaging will be discussed. 2.1. Digital holographic imaging: basics The first step of holographic imaging is wavefront recording and the second step is wavefront reconstruction in optical holography. Coordinate system for holographic imaging system is shown in Fig. 1. The object plane is located at xo yo , hologram plane is located at xh yh and image plane is located at xi yi . An image plane is

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S. Tan, S. Wang / Optik 124 (2013) 6611–6614

Fig. 2. Recording set-ups. (a) In-line holographic configure. (b) Off-axis holographic configure.

Fig. 1. Coordinate system for holographic imaging system.

separated by distance di from the hologram plane and object plane is separated by distance do from the hologram plane. R is reference wave. If reference wave is plane wave and its amplitude is A, using the paraxial or Fresnel approximation, the intensity of interference pattern recorded at the hologram plane xh yh is given by

+A

 +A

 exp(i2d/) ˆI (k, l) exp[id(m2  2 + n2 2 )] id M−1 N−1

ˆ n) = E(m,

k=0 l=0

× exp[−i2(kxh m + lyh n)] × exp

I(xh , yh ) = |O(xh yh |2 + A2



transformation is given by

exp −jkdo ∗ k 2 2 O (xo , yo ) exp{−j [(xh − xo ) + (yh − yo ) ]}dxo dyo −jdo 2do exp jkdo O(xo , yo ) exp jdo





j

k 2 2 [(xh − xo ) + (yh − yo ) ] 2do

dxo dyo

(1)

i

d



(k2 xh2 + l2 yh2 )

where m = 0, 1, 2, . . ., M − 1, n = 0, 1, 2, . . . N − 1,  = 1/(Mxh ),  = 1/(Nyh ). Using the convolution approach, the reconstruction of the hologram is expressed by ˆ E(m, n) = I−1 {I[Ih (m, n)r ∗ (m, n)] ∗ hf (m, n : di )}

where the wave length of the reference wave is , and k = 2/ is the wave number. The wavefront reconstruction process is to compute the field at an image plane separated by a distance di from the hologram plane as shown in Fig. 1. Optical field at the image plane is expressed as: exp(i 2di /) E(xi , yi ) = idi × exp

 i  di

(5)

(6)

where Ih (m,n) is optical field of holographic plane; I is Fourier transform; r*(m,n) is complex conjugate of reference wave; and hf (m,n:di ) is diffraction kernel or is called the point spread function(PSF) or the impulse response of the system. The

∞ ∞ I(xh , yh ) −∞−∞

(xi − xh )2 + (yi − yh )2



dxh dyh

(2)

The form of a two-dimensional (2D) linear convolution of Eq. (2) may be written as:

∞ ∞ E(xi , yi ) =

I(xh , yh )hf (xi − xh , yi − yh ; di )dxh dyh −∞−∞

= {I(x, Y ) ∗ ∗hf (x, y, di )}x=xi ,y=yi

(3) Fig. 3. Experiment set up.

where hf (x, y ; di ) is a 2D linear chirp function given by: hf (x, y; di ) =





i i 2 exp (x + y2 ) di di

(4)

Digital holography is different from conventional holography. In digital holography, the hologram is recorded in a charge-couple device (CCD) and the object is reconstructed using numerical methods. The numerical reconstruction is done by computer and therefore a discrete form of the reconstruction algorithms has to be implemented. Now, there are main two reconstruction algorithms: the Fresnel approximation and the convolution approach. It is assumed that the CCD is composed of M × N pixels distributed in a grid. Each pixel has a lateral extend of xh , yh in the x, y directions respectively. The discrete form of the Fresnel

Fig. 4. Schema of reconstructed algorithms on Matlab. (a)Fresnel approximation and (b) convolution Approach.

S. Tan, S. Wang / Optik 124 (2013) 6611–6614

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Fig. 5. Original hologram and reconstruction of copepod. (a) Original hologram. (b) Fresnel Approximation. (c) Convolution approach.

paraxial-approximated diffraction kernel is given by: hf [m, n; di ] = hf (mxh , nyh ; di ) =



i 1 2 2 exp (mxh ) + (nyh ) idi di

(7)

2.2. Recording set-ups Selecting the appropriate recording set-up in holographic experiment is very important step, which usually depends on the characteristics of the object to be imaged. Typically, recording setups are classified in-line and off-axis configurations, as shown in Fig. 2. For in-line holographic configure, both reference wave and the object wave are collinear and normal to the CCD plane. In-line holographic configure setup is shown in Fig. 2a. Because the structure of in-line holographic set-ups is simple, they are applicable for underwater imaging. In-line digital holography is the optimum choice for image plankton as it maximizes the fringe spacing produced at the hologram plane, but in some cases, spatial overlap occurs between the twin images and the DC term. However, this limitation has been recently overcome with some technology, such as Phase-shift algorithms for removing the artifacts introduced by DC term and the virtual image in the reconstruction. In off-axis holography, the interference pattern is recorded with a reference wave tilted by a small angle respective to the optical axis as shown in Fig. 2b. The main advantage of off-axis holography is that the DC term and the real and virtual images are spatially separated during the reconstruction. However, the structure of offaxis holographic set-ups is so complex that it is not suitable for underwater imaging. 3. An approach for sensing marine plankton using digital holographic imaging 3.1. Experiment system The experiment system about digital holographic imaging of marine plankton is designed as shown Fig. 3. In-line holographic configure is used in the experiment. As opposed to the off-axis set-up, in-line holographic configure is more suitable for the applications such as underwater imaging. As shown in Fig. 3, the hologram of Marine plankton is recorded in CCD. The recorded hologram contains information about the amplitude and phase of the optical field of marine plankton. The optical field is retrieved by numerical algorithms, which enable the reconstruction of the field at different distances relative to the detector from a single hologram. The experiment was carried out using the in-line singlebeam configuration. The illumination source consists of 10 MW helium–neon laser ( = 0.6328 ␮m). The point source produced by the pinhole generates a spherical wave that propagates toward a

collimating lens where the collimation takes place and the diameter of the collimated beam is 25 mm. The plane wave produced after collimation illuminates approximately 21 ml of seawater while the dimensions of the culturing tank are 32.5 mm × 50 mm × 13 mm. The field of view of the system was imposed by the finite size of the CCD (12.3 mm × 12.3 mm); the CCD selected for our underwater digital holographic camera is 1M30 from DALSA; the pixels size of CCD is 12 ␮m; the number of pixels is 1024 × 1024 pixels. The CCD is connected to an evaluation board which communicates with a computer via the frame grabber VIPER-DIGTIAL card. The holograms which are captured are stored in Bitmap format. In this experiment, we selected copepods as sample. 3.2. Experiment result Finally, the holograms are reconstructed using the following algorithms on a computer. Fig. 4 shows the schema of reconstructed algorithms process on a computer, where f is the focal length of virtual lens. Fig. 5a shows a typical digital hologram of copepods from an experiment. Fig. 5b and c shows reconstructions made by Fresnel approximation and convolution approach. It is clear from these images that small features of copepods can be resolved, such as the antennas. This information is generally sufficient to develop a taxonomical classification of the specimen. Here, reconstruction of a copepod was used the in-line set-up with He–Ne laser and image plane was separated by a distance 1.2 m from the hologram plane. 4. Conclusion This paper focuses on some issues encountered in the implementation sensing of marine plankton based on digital holographic imaging. The process consists of: (1) digital holographic imaging for sensing marine plankton and (2) numerical reconstruction of marine plankton hologram. Thus, we can obtain the recorded optical field of marine plankton. This approach for sensing marine plankton using digital holographic imaging is an extremely valuable technique for the study of marine plankton fields as it allows instantaneous, noninvasive, high-resolution recording of substantial volumes. It is very helpful for study of marine plankton. Acknowledgment This work was supported by The National High Technology Research and Development Program of China (863 Program) (No. 2010AA092205). References [1] C. Knox, Holographic microscopy as a technique for recording dynamic microscopic subjects, Science 153 (1966) 989–990. [2] C. Knox, R.E. Brooks, Holographic motion picture microscopy, Proc. R. Soc. London, Ser. B 174 (1969) 115. [3] G.L. Stewart, J.R. Beers, C. Knox, Application of holographic techniques to the study of marine plankton in the field and in the laboratory. Developments in

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