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Underwater spatially, spectrally, and temporally resolved optical monitoring of aquatic fauna

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Abstract

A continuous-wave (CW) Scheimpflug underwater multi-spectral lidar system was constructed to monitor aquatic fauna with spatial, spectral, and temporal resolution. Utilizing a 1 W 414 nm diode laser and a detection set-up with a reflective grating, measurements of shrimp pleopod movements at fixed range, and the swimming of small fish trapped in a clear tube were performed in a 5 m ×0.6 m ×0.6 m water tank. The spatial resolution is about 5 mm, the spectral resolution is 10 nm (from 400 nm to 700 nm), and with proper binning of the CCD, a read-out repetition rate up to 150 Hz can be reached. The experimental results demonstrate that the underwater Scheimpflug lidar system has great potential for detailed monitoring of the small aquatic fauna in oceanic environments.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The ocean is the largest ecosystem on the earth and accounting for 71% of the total area of the planet [1]. It is of great importance and necessity to study and care for the oceanic environment and make better use of the natural resource it represents. Observing the behavior of an individual fish or shrimp constitutes an elementary and important element of studying the oceanic biological creatures as part of, e.g., biotics studies [2,3], as well as for the economic aspects of fisheries [4]. Assessing the quantity and distribution of fish and shrimps in a certain volume of water has bearing on the biological quality in the ocean environment [57]. A variety of research methods have been adopted to retrieve useful information to describe the aquatic fauna in the ocean environment, e.g., sampling by trawler [8], sonar sounding [9,10], visual observation [11,12], or computer vision adaption [13,14]. The common and traditional ways of study are laborious, time-consuming, and non-in-situ. Camera recordings can achieve high spatial resolution at short distance. Holographic cameras need more sophisticated detectors and long-time processing of the data recorded. The sonar technologies can achieve large-area monitoring at moderate spatial resolution (about 0.1 m). However, light detection and ranging (lidar) methods become very powerful remote sensing tools to meet the need for aquatic environmental monitoring with its high-precision and appreciable penetration through water. Utilizing the relatively high transmission of the laser beam in the blue-green band, airborne time-of-flight lidar systems can detect underwater targets at distances up to 50 m beneath the surface [15], as demonstrated by, e.g., the AOL [16], SHOALS [17] and Mapper 5000 systems [18]. Taking advantage of the rapid development of high-power diode lasers and readily available low-cost telescopes, a CW lidar approach using a Scheimpflug arrangement could recently be developed [19]. A wide range of applications has been successfully performed with Scheimpflug lidar systems in ecological and environmental monitoring, e.g., monitoring of atmospheric aerosol pollution [2022], aquatic zooplankton, phytoplankton [23], and insects [24,25], terrestrial vegetation [26] and even flames [27]. A review of optical techniques to study aquatic and atmospheric fauna was recently published [28].

We are now presenting a novel and compact underwater hyperspectral Scheimpflug lidar system for aquatic fauna monitoring. Different from a previous set-up using a transmission grating [23], a reflective grating, instead of the complicated prism-grating-prism (PGP) structure used as the dispersion component, was adopted in a more compact design to perform aquatic fauna monitoring measurements in a 5 m-length in-door water tank, revealing the detailed movements of shrimps and fish. To our knowledge, this is the first lidar-type demonstration of the related oscillatory signals in the aquatic environment, corresponding to wing-beat assessments of flying insects (see, e.g., [19,25].) The studies of dynamic behavior are enabled by the fast read-out capability (typically 100 Hz) of our detector, which also provides spatial and spectral resolution.

Needless to say, with the capability of our system of elastic-scattering as well as fluorescence monitoring, it is also perfectly adapted for the less demanding task of pollution studies in the oceans, which become increasingly contaminated. In particular, plastics with very characteristic fluorescence, might by 2050 be more present than fish in the maritime environment [29] and can be readily studied, as well as fluorescence from excess algae, which indicate eutrophication.

2. Principles and methods

The reflective under-water Scheimpflug hyperspectral lidar system, which consists of a transmitting unit and a receiving unit, is shown in Fig. 1(a). The transmitting unit consists of a 1 W 414 nm diode laser (XinRui, FB04) and a laser expander (adjustable focal length 16-48 mm, CW-VM1648-10MP). The laser wavelength is chosen considering the comparatively low absorption of water in the blue-green region, achieving efficient excitation of chlorophyll from algae, and commercial availability. The receiving unit, as shown in Fig. 1(b), includes a 50 mm-diameter dual-glue lens (f = 200 mm, Edmund Optics, 45179) to collect the scattered light signal from the target, a 300 grooves/mm grating (Edmund Optics, 64398) to spectrally resolve the collected light, and an area-array CCD (AVT, MANTA-283B) to image the light path. The size of the active imaging area is 8.8 × 6.6 mm2, corresponding to 1936×1458 pixels (horizontal × vertical) with a pixel size of 4.54 µm×4.54 µm. The field of view (FOV) is about 3 degrees. First, the light from the target area is collected by lens 1 and is focused on the tilted slit 2 to suppress the background disturbance. Then the light is collimated on the reflective grating 4 by the reflective mirror 3. After spectral dispersion, the light is focused by the reflective mirror 5 and proceeds through the collimating units 6 onto the image plane of the CCD 7. Before the CCD image plane, a long-pass optical filter (450 nm) is inserted to reduce the strong elastically scattered light. The slit is in our arrangement tilted 65 degrees with regard to the optical path, and the angle between the laser beam and the optical axis of the receiver is about 2 degrees. The slit width is about 200 µm resulting in a spectral resolution of about 10 nm. In a previous set-up [23], a transmission grating sandwiched between two prism wedges (PGP) was used as the spectral unit. Due to the larger blaze angle (17.5 degrees) of the transmission grating than the one of the presently used reflective grating, two extra prism wedges are needed for the light path formation. However, in the present reflective grating, the blaze angle of 4.3 degrees eliminates the need of the two prism wedges, resulting in a more compact and more easily adjustable structure.

 figure: Fig. 1.

Fig. 1. (a) 3D modelling of the underwater Scheimpflug lidar. The CW laser transmitter is in the upper right part. (b) Optical layout of the receiving system plotted in Zemax (1. Collecting lens, 2. Slit of 200 µm in width and 30 mm in length, 3. Reflective mirror, 4. Reflective grating, 5. Reflective mirror, 6. Collimating lens units, 7. Imaging CCD).

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Our system was arranged outside the end of an in-door 0.5 m x 0.5 m x 5.0 m water tank, with laser beam transmission and backscattered light recording through the end glass window. Calibration of our system was accomplished by moving spatially and spectrally well-defined objects along the laser beam in the tank, before measurements of aquatic fauna interacting with the beam were performed.

By tilting the image plane, in an optical arrangement named after Theodor Scheimpflug [30], a sharp focus along the whole main optical path (object plane; in our case the transmitted laser beam) can be achieved when the intersection of the image plane, the lens plane and the object plane coalesce in one point. To better understand the Scheimpflug principle, we refer to Fig. 2.

 figure: Fig. 2.

Fig. 2. Schematic diagram of the Scheimpflug principle. The angle between the image plane and the lens plane is $\theta $. The angle between the lens meridian plane and the object plane is $\beta $. The focal length of the lens is f. O is the center of the lens and $O^{\prime}$ is the center of the CCD imaging detector. The distance between the center of the lens and the center of CCD is ${L_c}$ ($OO^{\prime} = {L_c}$). The distance between the center of the lens to the object plane is the baseline L ($OO^{\prime\prime} = L$). The range to the target is r. $AB$ is the length of the CCD, e.g., the longer length of an area CCD. $A^{\prime}B^{\prime}$ is the length of the laser beam corresponding to $AB$ on the detector. Taking point A as an example, the distance between A and the lens plane is $l^{\prime}$. The distance between $A^{\prime}$ and the lens plane is l. $\alpha $ is the angle between $AA^{\prime}$ and $SA$. We assume there is a pixel in the CCD array which is along $AB$ and the distance between this pixel to the CCD center $O^{\prime}$ is p.

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Based on the geometrical and optical conditions in Fig. 2, and the parameters defined there, we can obtain the following relationships, as expressed in Eq. (1) to Eq. (4).

$$\frac{1}{l} + \frac{1}{{l^{\prime}}} = \frac{1}{f}$$
$$l^{\prime} = psin\theta + {L_c}$$
$$tan ({\alpha - \beta } )= \frac{{pcos\theta }}{{psin\theta + {L_c}}}$$
$$tan \alpha = \frac{L}{r}$$
With these equations, the range to the object r can be further expressed by Eq. (5) with the pixel position.
$$r = \frac{{L[{p({sin\theta - cos\theta tan\beta } )+ {L_c}} ]}}{{p({cos\theta + sin\theta tan\beta } )+ {L_c}tan\beta }}$$
During experiments, we can calibrate $\beta $ by recording an artificial target with known distance ${r_{cal}}$ and the detected pixel position ${p_{cal}}$. Thus $\beta $ can be further presented with Eq. (6).
$$\beta = arctan\frac{L}{{{r_{cal}}}} - arctan\frac{{{p_{cal}}({{r_{cal}} - f} )}}{{{r_{cal}}f}}$$
For a more detailed equation derivation, we refer to [20,21].

Based on the geometric relationship to fulfill the Scheimpflug condition as seen in Fig. 2, a simulation of the equations is programmed with Matlab. In spatial calibration measurements, 24 different distances, with the separation of 100 mm, from 2700 mm to 5000 mm, were recorded and were found to have very good agreement with the simulated curve presented in Fig. 3(a). Five different fluorescent samples were measured with a compact spectrometer (Ocean Optics USB4000) for the spectral calibration using a 414 nm excitation laser. The calibration fitting curve is presented in Fig. 3(b). One frame taken by the CCD of a plastic fishing line with orange fluorescent paint is presented in Fig. 4(a) with the horizontal pixels in Fig. 4(b) and vertical pixels in Fig. 4(c) indicating the spatial distribution and spectral distribution, respectively. To increase the CCD frame rate, the vertical pixels are binned to 200 corresponding to a frame rate of 100 fps.

 figure: Fig. 3.

Fig. 3. (a) Relationship between pixels and distance as calculated with relevant parameters plotted as a black solid line, Measured data are plotted with blue circles and its fitting curve is plotted as a red dashed line; (b) Relationship between pixels and wavelengths plotted as red circles. A fitting curve is plotted as a blue dashed line.

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 figure: Fig. 4.

Fig. 4. (a) One frame for a plastic fishing line with fluorescing orange paint, recorded by the underwater Scheimpflug lidar. The signals indicated with two white arrows come from the painted fish line in the elastic region and the longer wavelength fluorescence region. The signal at further distance is the elastic signal from the tank end; (b) Spatial distribution retrieved from (a), vertically averaged from wavelength pixel 70 to pixel 80; The combined elastic and fluorescence signal of the fish line is much narrower than the signal from the tank end, which is due to the diameter of the fish line being much smaller than the foot print of the the laser beam impinging of the tank end. (c) Spectral distribution of the fish line, corresponding to the position of the dotted white line in (a), horizontally averaged from distance pixel 910 to pixel 920.

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3. Measurements and results

Initial preliminary measurements were made on a man-made target where 2 pieces of fishing line fibers (10 mm in length) were glued to the head of an electronic tooth brush, with one line coated with fluorescing orange paint and the other one with green fluorescing paint. The diameter of each fishing line was around 0.185 mm. The electric tooth brush head vibrated at the frequency around 100 Hz. We put the brush into the light path 3 m away from the system in the water tank and the frequency of its vibration could be recorded by our system as presented in Fig. 5(a). The frame rate of the CCD was set to about 100 Hz. For each frame (1936×200, H×V), only an area of 100×200 (H×V) is selected corresponding to the fishing line fibers at 3 m distance. In the results of Fig. 5(a), there actually are 200 frames put together chronologically because each frame has a width of 100 pixel. By recording all the signal in a time sequence, we realized monitoring of the vibration of the targets. In the period of every 10 frames, 10 pair of signals from the two fibers could be found. Shown in the zoom-in graph in Fig. 5(b), in the range from 8000 to 9000 (frame×100), 10 random pairs of the fishing line fiber signals can be observed, e.g., 6 green signals and 4 orange signals. The vibration frequency can be derived to about 100 Hz. The vibrations of the small fishing line could simulate the movements of pleopod legs, e.g., belonging to a shrimp.

 figure: Fig. 5.

Fig. 5. (a) Continuous imaging of the fibers attached to the vibrating head; (b) Zoom-in on a section of the data. Elastic scattering at 414 nm as well as fluorescence in the green and orange regions are observed, as vibrating fibers sequentially enter the observation field-of-view.

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From studies of shrimp movements, it is known that there are mainly two kinds of swimming modes of normal shrimp species: swimming by pleopod movement and swimming by tail movement. In most circumstances, the shrimp adopts the former way to swim with its five pairs of pleopods. Literature values of the frequency of the movement of the pleopods are ranging from 2 Hz to 6 Hz [31]. However, when the shrimp feels danger from the surroundings, it will bend over its whole tail and jump at a glance, resulting in a displacement of 1.5 to 2 times its body length [32]. In the traditional monitoring method of shrimp swimming behavior, the shrimps are trapped in a water tank and a high-speed camera is used to record their movements. Then, the results are manually evaluated by observing each frame, which is time-consuming and of low efficiency. In our measurements using the underwater Scheimpflug lidar system, we tried to realize monitoring of the movement frequency of the shrimp pleopods by continuous recording the elastic signals. Fresh-water shrimps (Metapenaeus Ensis (De Hann)) as presented in Fig. 6(a) were acquired from a local market and we monitored movements of their pleopods at a fixed distance of about 3 m away from the system as seen in Fig. 6(b). The movements of the shrimps were also recorded with a commercial camera at a frame rate of 15 fps as shown in Fig. 7. The sample shrimp is about 50 mm in length.

 figure: Fig. 6.

Fig. 6. (a) Photo of a studied shrimp with 5 pairs of labelled pleopods; (b) Schematic drawing of the measurement of the movements of the pleopods of the shrimp, which was fixed in the tank at a distance of 3 m from the underwater Scheimpflug lidar system, with the laser beam closely passing below.

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 figure: Fig. 7.

Fig. 7. Photos of movements of a shrimp, continuously recorded by a camera in a time sequence from (a) to (i).

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From the 9 continuously recorded photos in Fig. 7, which accounts for a total duration of 0.6 s, the swimming movements of the 5 pairs of pleopods of a shrimp can be inferred. The pleopods from head to tail can be assigned numbers from 1 to 5 as shown in Fig. 6(a). In the continuous recordings of the shrimp freely swimming, the first 3 pairs of pleopods start to move from head to tail and when these 3 pairs reach the middle of the body, the other 2 pairs of pleopods start to move from tail to head. Next, when the first 3 pairs reach the shrimp belly, the other 2 pairs also arrive the same region. Then the cycle starts again. Thus, we find that the 5 pairs of pleopods from head to tail start to move with a small delay between the former pair and the latter pair. From the study of the movements of the shrimp pleopods, the pleopod signals appear to be periodic as shown in Fig. 7. The moving frequency f of the pleopods could be derived by the expression given in Eq. (7).

$$f = \frac{{{f_{ps}}}}{n}$$
Here fps is the frame number per second of the camera and n is the number of the frames to complete one cycle.

Based on these photos, we find that a full cycle corresponds to a time period of 4 continuously recorded frames (Fig. 7(a)-(d)) and a subsequent time period of 3 continuously recorded frames (Fig. 7(d)-(f)), etc. The frame rate of the camera is about 15 fps. Thus, the movement frequency of the pleopods is evaluated to about 3.75 Hz and 5 Hz, respectively, in two subsequent cycles. By photographing the movements of the 5 pairs of pleopods, we can better understand the results recorded by our underwater Scheimpflug lidar system, as described below.

Results of measurements on three typical sample shrimps (shrimp A, B, C) with our underwater Scheimpflug lidar system are shown in Fig. 8. As presented in Fig. 8 (A(2)), in the period of 200 frames, 10 cycles (each cycle contains 3 signals featuring the main pleopods) are observed. Thus, it takes 20 frames to complete one cycle. The frame rate of the CCD is 116 fps in these measurements. Then the movement frequency can be derived according to Eq. 7; the frequency is about 5.8 Hz. In Fig. 8 (B(2)), in the period of 200 frames, there are 11 cycles of movements. The movement frequency of shrimp B is then about 6.4 Hz according to Eq. 7. Similarly, the movement frequency of shrimp C is about 6.3 Hz. Compared with the traditional manual recognition of the shrimp pleopod movements, the observation by our system could be more accurate and efficient.

 figure: Fig. 8.

Fig. 8. Continuous recordings of the elastic signals of the pleopod movements of three shrimps (A)-(C) and their zoom-in graphs of recordings.

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Further, we monitored small orange fresh-water fish, Brachydanio rerio, (about 1 to 3 cm in length) with the underwater Scheimpflug lidar system. They were trapped in a clear plastic tube (55 cm in length and 5 cm in diameter) made of plastic and suspended in the water tank in our laboratory as seen in Fig. 9. This setting allows the fish to swim freely inside the tube. Due to the strong reflection signals from the two plastic end caps of the tube, the fluorescence signal instead of the elastic signal from the orange small fish are used to track their movements to avoid the interference from the caps. The camera frame rate was now set to 118 fps corresponding to 104 vertically-binned pixels. The detection laser beam width was about 3 cm in diameter so as to let the whole fish body be illuminated by the laser. The raw frames were linearly enhanced to get better contrast.

 figure: Fig. 9.

Fig. 9. (a) Schematic drawing of the trap suspended inside the water tank; (b) Photo of the fish trap suspended inside the water tank during the measurement.

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In the results presented in Fig. 10, we can monitor the movement of the fish tail by continuous recording. In Fig. 10 (A(2)), during 60 frames, three signals as labelled with numbers can be captured and the frequency of the fish tail of fish A can be calculated as about 6 Hz. Similarly, the fishtail frequency of fish B is about 5 Hz, and 4 Hz for fish C as well as for fish D. Besides, during the periodic signals, there are obvious small spikes between two signals as marked with white arrows in Fig. 10 (C(2)) and (D(2)). The spikes signals are profiling the signals from the chest fins of the small fish. The swimming behaviour of the fish can be interpreted from the combination of signals of the fin and the body. Then the movement frequency of the fins can be estimated. From the recordings, we can also infer whether the fish swam across the laser beam or swam along the laser beam. E.g., the signal span for fish A is shorter which means that the fish is swimming across the laser beam. The signal span for fish C and fish D is longer and the continuous signal path could describe the swimming path of the fish along the laser light path. More details are given in the figure caption.

 figure: Fig. 10.

Fig. 10. Continuous recordings o fluorescence signals from the movements of four small fish (A)-(D) and zoom-in graphs of recordings. The slopes of the signal in (A(2)) and (B(2)) are different as time passes, which means that fish (A) is swimming across the detection laser beam from far distance towards close distance to the detector, and fish B swimming in the reverse direction. The high intensity signals are from the fish body when the fish swam across the laser beam with more area exposed to the detector. In (C(2)) and (D(2)), the continuous periodic signals can be seen as the fish swimming inside the detection laser beam and the signals became weaker since less area of the fish was exposed to the detector. The periodically-appearing spikes as indicated with the white arrows are from the chest fins of the fish. Due to the tilted detector of the Scheimpflug setting, there is an angle between the laser beam and and the optical path of the detector. During the fish swimming by swaying its tail from right to left, the fish head was not always vertically towards the detector, which resulted in the curving of the continuous signals. There is a break between two continuous signals in (D(2)) indicating that the fish swam outside the laser beam. However, on both sides of the break, two strong signals (from the body), as marked with dotted circles, can be noted, which result when the fish turned around with more area exposed to the detector.

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4. Conclusions

Our underwater Scheimpflug lidar system has demonstrated the ability to monitor dynamics in the aquatic fauna in an experimental water tank. By analyzing the results of continuous recordings, the vibration frequency of man-made, motor-driven fibers (0.185 mm in diameter and 10 mm in length), and the movement frequency of shrimp pleopods and fishtails (fish of 1-3 cm length) have been captured. The detectable object size ranges from about 0.2 mm to 3 cm in the present implementation. This system provides a viable method for in situ, non-invasive, real-time monitoring of the aquatic fauna in a different way than available with traditional research methods of aquatic environmental monitoring. The system, with elastic scattering as well as fluorescence detection capability, is also well adapted for plastics monitoring is the oceans, which become more and more polluted with the amount of plastics soon expected to supersede the fish contents.

All the measurements were performed in an in-door water tank filled with tap water. However, our system is rugged and is well suited for field work. Actually, a different light-weight Scheimpflug system was earlier successfully tested by us for vegetation profiling from a commercial drone [26]. Thus, with suitable adaption, our new aquatic system could be installed on underwater platforms, such as ROVers (Remote Operated Vehicle) [33,34] to provide so far inaccessible information also in an imaging mode. Such work is now in the planning phase, also considering different water conditions, regarding, e.g., stratification and turbidity.

Funding

National Science and Technology Infrastructure Program (2018YFC1407503); National Natural Science Foundation of China (61705069); Foundation for Distinguished Young Talents in Higher Education of Guangdong.

Acknowledgments

The authors gratefully acknowledge the support from Professors Sailing He and Guofu Zhou.

Disclosures

The authors report no conflicts of interest.

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Figures (10)

Fig. 1.
Fig. 1. (a) 3D modelling of the underwater Scheimpflug lidar. The CW laser transmitter is in the upper right part. (b) Optical layout of the receiving system plotted in Zemax (1. Collecting lens, 2. Slit of 200 µm in width and 30 mm in length, 3. Reflective mirror, 4. Reflective grating, 5. Reflective mirror, 6. Collimating lens units, 7. Imaging CCD).
Fig. 2.
Fig. 2. Schematic diagram of the Scheimpflug principle. The angle between the image plane and the lens plane is $\theta $ . The angle between the lens meridian plane and the object plane is $\beta $ . The focal length of the lens is f. O is the center of the lens and $O^{\prime}$ is the center of the CCD imaging detector. The distance between the center of the lens and the center of CCD is ${L_c}$ ( $OO^{\prime} = {L_c}$ ). The distance between the center of the lens to the object plane is the baseline L ( $OO^{\prime\prime} = L$ ). The range to the target is r. $AB$ is the length of the CCD, e.g., the longer length of an area CCD. $A^{\prime}B^{\prime}$ is the length of the laser beam corresponding to $AB$ on the detector. Taking point A as an example, the distance between A and the lens plane is $l^{\prime}$ . The distance between $A^{\prime}$ and the lens plane is l. $\alpha $ is the angle between $AA^{\prime}$ and $SA$ . We assume there is a pixel in the CCD array which is along $AB$ and the distance between this pixel to the CCD center $O^{\prime}$ is p.
Fig. 3.
Fig. 3. (a) Relationship between pixels and distance as calculated with relevant parameters plotted as a black solid line, Measured data are plotted with blue circles and its fitting curve is plotted as a red dashed line; (b) Relationship between pixels and wavelengths plotted as red circles. A fitting curve is plotted as a blue dashed line.
Fig. 4.
Fig. 4. (a) One frame for a plastic fishing line with fluorescing orange paint, recorded by the underwater Scheimpflug lidar. The signals indicated with two white arrows come from the painted fish line in the elastic region and the longer wavelength fluorescence region. The signal at further distance is the elastic signal from the tank end; (b) Spatial distribution retrieved from (a), vertically averaged from wavelength pixel 70 to pixel 80; The combined elastic and fluorescence signal of the fish line is much narrower than the signal from the tank end, which is due to the diameter of the fish line being much smaller than the foot print of the the laser beam impinging of the tank end. (c) Spectral distribution of the fish line, corresponding to the position of the dotted white line in (a), horizontally averaged from distance pixel 910 to pixel 920.
Fig. 5.
Fig. 5. (a) Continuous imaging of the fibers attached to the vibrating head; (b) Zoom-in on a section of the data. Elastic scattering at 414 nm as well as fluorescence in the green and orange regions are observed, as vibrating fibers sequentially enter the observation field-of-view.
Fig. 6.
Fig. 6. (a) Photo of a studied shrimp with 5 pairs of labelled pleopods; (b) Schematic drawing of the measurement of the movements of the pleopods of the shrimp, which was fixed in the tank at a distance of 3 m from the underwater Scheimpflug lidar system, with the laser beam closely passing below.
Fig. 7.
Fig. 7. Photos of movements of a shrimp, continuously recorded by a camera in a time sequence from (a) to (i).
Fig. 8.
Fig. 8. Continuous recordings of the elastic signals of the pleopod movements of three shrimps (A)-(C) and their zoom-in graphs of recordings.
Fig. 9.
Fig. 9. (a) Schematic drawing of the trap suspended inside the water tank; (b) Photo of the fish trap suspended inside the water tank during the measurement.
Fig. 10.
Fig. 10. Continuous recordings o fluorescence signals from the movements of four small fish (A)-(D) and zoom-in graphs of recordings. The slopes of the signal in (A(2)) and (B(2)) are different as time passes, which means that fish (A) is swimming across the detection laser beam from far distance towards close distance to the detector, and fish B swimming in the reverse direction. The high intensity signals are from the fish body when the fish swam across the laser beam with more area exposed to the detector. In (C(2)) and (D(2)), the continuous periodic signals can be seen as the fish swimming inside the detection laser beam and the signals became weaker since less area of the fish was exposed to the detector. The periodically-appearing spikes as indicated with the white arrows are from the chest fins of the fish. Due to the tilted detector of the Scheimpflug setting, there is an angle between the laser beam and and the optical path of the detector. During the fish swimming by swaying its tail from right to left, the fish head was not always vertically towards the detector, which resulted in the curving of the continuous signals. There is a break between two continuous signals in (D(2)) indicating that the fish swam outside the laser beam. However, on both sides of the break, two strong signals (from the body), as marked with dotted circles, can be noted, which result when the fish turned around with more area exposed to the detector.

Equations (7)

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1 l + 1 l = 1 f
l = p s i n θ + L c
t a n ( α β ) = p c o s θ p s i n θ + L c
t a n α = L r
r = L [ p ( s i n θ c o s θ t a n β ) + L c ] p ( c o s θ + s i n θ t a n β ) + L c t a n β
β = a r c t a n L r c a l a r c t a n p c a l ( r c a l f ) r c a l f
f = f p s n
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