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A combination of physical and simulated results have been used to demonstrate that digital holography provides a suitable method for the 3D localisation of mosquitoes in a large field of view compared to similar previously reported digital holographic applications. The expansion on previous work on the assessment of effective pixel size vs localisation error and minimum resolvable distance between two objects provided the parameters to design a physical experimental large field of view setup (240 × 240 × 1000 mm). Intensity reconstructions of a free-flying mosquito recorded using this setup indicate that finer features of a moving mosquito can be defined, and the mosquito can be localised in 3D coordinates in a large field of view. Simulations allowed for a large number of data points to be collected on object localisation of a mosquito obscured by a bednet, and the upper z-axis resolution limit of the background removal technique was defined. The use of physical data to validate the method and assess the lower z-axis resolution limits indicate that the methods presented in this paper perform well with real data.
The use of an effective pixel size (imaging resolution) throughout this manuscript allows the recording volume to be scalable in terms of optical hardware components. When scaling the optical hardware, the effective pixel size, wavelength, and mosquito size are retained. However, by using a camera with a larger number of pixels, high-quality Fresnel lenses or holographic optical elements may provide a method to scale the recording volume to a larger size. However, it is suspected that a Fresnel lens would produce a large amount of forward scattering onto the hologram that would likely impact on the reconstruction and localisation accuracy of a mosquito. A feasibility study on the use of Fresnel lenses and/or holographic optical elements as a hardware option for increasing the recording volume will be conducted in future work.
Table 1 summarises the physical results presented earlier in the paper in terms of minimum resolvable distance between a bednet and a mosquito and mean localisation error for the two proposed z-axis localisation methods and each of the EPS values.
Method CCoFM Background Removal Resolvable
≥ zs, mmMean
zerr, mmResolvable
≥ zs, mmMean
zerr, mmΔxe = 58.60 µm 35 9.22 3 2.75 Δxe = 78.13 µm 50 9.23 3 4.75 Δxe = 97.67 µm 60 10.78 45 9.04 Table 1. Largest unresolvable z-axis separation and mean localisation error for the two proposed z-axis localisation methods and three effective pixel sizes - physical results.
The background removal of bednet can be used when precise mosquito-bednet 3D tracking very close to the bednet is required, but is strictly limited by the condition that the bednet cannot move between the bednet-only hologram being recorded and the end of the main recording of mosquito-bednet interaction. This limitation could be relaxed using a moving frame subtraction technique, although this method would not be suitable if the mosquito is resting, crawling, or moving very slowly in the lateral direction, as the diffraction patterns will subtract from one another. Examining the interaction between mosquitoes and holes in the surface of a bednet (a typical fault after regular bednet usage) is one potential application. A previous study used a method of having a very short depth of field that only covered the thickness of the net in the z-direction34. The mosquito would therefore go in and out of sharp focus as it crosses the XY plane of the hole. This paper examines the time between a mosquito entering a dwelling to successfully passing through the bednet hole but does not explore the flight kinematics in detail. The lack of true 3D positional data makes it difficult to determine if the mosquito is randomly bouncing or searching the bednet through subsequent contacts, or not making contact at all. The background removal method could improve a study such as this. The background removal has other novel biological applications: the process enables the 3D kinematics of a mosquito approaching a bednet to be accurately described up to the surface of a net (2D imaging has an error in the unknown third axis), as well as accurately recording insecticide dosages to a mosquito freely interacting with an insecticide-soaked net (rather than lab-based in-vitro insecticide dosage tests).
Fig. 9a, b show reconstructed images of the same mosquito from a mosquito-bednet hologram after bednet subtraction and without subtraction, respectively. In both cases, the mosquito was positioned
$ z_s=20 $ mm behind the bednet and recorded at an EPS of$ \Delta{x}_e=78.13 $ µm. Accurate reconstruction of the finer features of the mosquito, such as its wings, body, and legs, may make orientation calculations possible in future work, which may give further insights into mosquito-bednet-hole interaction. Fig. 9c, of the same mosquito not obscured by a bednet, is shown for qualitative comparison.Fig. 9 Intensity reconstruction of a mosquito located
$ z_s=20 $ mm behind a bednet positioned at$ z=1.40 $ m a with and b without background net subtraction. c Reconstruction of the same mosquito recorded with no bednet (mosquito-only hologram). d Diagram to show sampling of diffracted wavefront with smaller and larger EPS.It is interesting to note the large change in minimum resolvable distance for the background removal method between EPS values of
$ \Delta{x}_e=78.13 $ µm and$ \Delta{x}_e=97.67 $ µm. As previously discussed, the EPS determines the sampling rate for which an interference pattern of a hologram is recorded and stored - Fig. 9d shows this qualitatively. The recorded diffraction pattern on the hologram plane is the superposition of the diffracted waves from: the mosquito, the bednet, plus the undisturbed reference wave. It is well known that the spatial extent in the XY plane of a diffraction pattern for a given object size increases as propagation distance increases. Therefore, increasing the object-to-hologram distance or, in this case, the mosquito-to-bednet distance may provide better distinction at the hologram between bednet and mosquito. Recording at a lower sampling rate (higher EPS) averages the combined signal, and if the Nyquist limit lies at an EPS value between$ \Delta{x}_e=78.13 $ µm and$ \Delta{x}_e=97.67 $ µm, the finer multi-object interference fringes between the mosquito and the bednet at lower z-axis separations may be lost. Further investigation into this, to determine if a critical$ \Delta{x}_e $ exists, may be conducted in future work.The minimum resolvable distance for the CCoFM method increases between each of the EPS values of 58.60 µm, 78.13 µm, and 97.67 µm, which is in-line with the result shown in Fig. 1 and was expected due to the decreasing Q-value in the single object focus metric curves as EPS increases. With a decreased Q-value, the superposition of two distinct curves into a single curve occurs at a larger z-axis separation and so a larger minimum resolvable distance is expected.
The CCoFM provides a methodology that is inherently temporally stable, as bednet background removal is not conducted and therefore movement of the bednet throughout the duration of a hologram time-series video recording will not influence the reconstruction and calculation of the focus metric curve. The downside of this method is that there are minimum resolvable distances between the bednet and mosquito, so accurate determination of close contact mosquito-bednet interaction is lost as the CCoFM second-pass focus metric becomes a curve with a single maxima. Fig. 10a shows the XY position of a dead mosquito manually moved in the XY plane over 30 frames (1 second) of a recorded video, where the z-axis position of the mosquito relative to the bednet was approximately
$ z_s=20 $ mm throughout the recording. Fig. 10b shows the CCoFM second-pass curves corresponding to three distinct frames, indicating a single peak for the mosquito-bednet reconstruction, meaning that resolving the two separate objects in the z-axis was unsuccessful using this method at this z-axis separation.Fig. 10 a Time-series XY positions of a manually moved mosquito located
$ z_s\approx20 $ mm behind a bednet positioned at$ z=1.40 $ m. b Tamura of Intensity focus metric (stars) and second-pass cross-correlation (squares) displaying a single peak (Frames 1, 15, 30).Although the z-axis separation was not resolved in the case above, it can be concluded that a mosquito localised in XY featuring a single maxima in the second-pass CCoFM curve is located at
$ z_{mos}<z_{res} $ , where$ z_{res} $ is the minimum resolvable distance of that particular setup as shown in Table 1. A time-series mosquito position dataset with this condition included would allow a single mosquito to be tracked pre-, during, and post- bednet interaction even though the precise 3D interaction for$ z_{mos}<z_{res} $ would not be determined. In previous studies, mosquito behaviour has been quantified into distinct categories, with movement close to the bednet below a certain velocity threshold classified as ‘resting’37. The CCoFM method combined with an appropriate tracking algorithm could therefore be useful in accurately determining resting time(s) and estimating a pseudo-dosage of insecticide that a mosquito receives.In this paper, we have demonstrated that digital holography offers the potential to examine 3D mosquito flight behaviour in a large volume where conventional imaging systems may be less effective. A physical experimental setup for the large field of view (240 × 240 × 1000 mm) recording of in-line digital holograms was presented. Intensity reconstructions of mosquitoes in full-flight were also presented, demonstrating that 3D localisation of a flying mosquito and reconstruction of smaller fast-moving features, such as the legs, body, and wings, was possible using digital holographic techniques. Applying this methodology to a time-series of holograms allows the accurate determination of mosquito tracks in 3D coordinates. Simulations and physical data were used to examine the concept of localisation of a mosquito obscured by a bednet, as accurately determining mosquito-bednet interaction is of particular biological importance in the development of intervention methods to reduce malaria transmission in humans. A novel Cascade-Correlation of Focus Metric was introduced for the accurate reconstruction and localisation of a mosquito occluded by a bednet and compared to a simple bednet subtraction technique. The benefits and limits of each approach were considered with regards to, experimental design, z-axis resolution limits, and upper limits for mosquito-bednet distance. Potential biological applications were also discussed, and it is anticipated that biologically significant experiments will be performed in future work. The result of this study is a scalable digital holographic methodology to examine mosquito flight in 3D at a level of accuracy previously only seen in 2D imaging of a smaller volume, and the ability to resolve 3D mosquito-bednet interaction of mosquitoes occluded by a bednet for the first time. For accurate and reliable kinematic analysis of mosquito flight close to a bednet, detailed 3D imaging is crucial to correct errors in the unknown third axis that are present when using 2D imaging, and digital holography offers a potential solution.
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A continuous wave 130 mW CrystaLaser DL785-150-SO with a wavelength of 785 nm provides illumination of the scene by expanding and spatially filtering the beam through an objective lens and aperture (expansion optics, EO). Two neutral density filters are placed between the laser head and spatial filter, consisting of OD = 1.5 and OD = 0.3, which reduces transmission of light to 1.7%, equating to approximately 2 mW of power. This would allow a theoretical increase in area of 64 × (8 × radius) if utilising the full 130 mW of laser power available for the same power density interacting with the object.
The collimating optic (CO) provides plane wave illumination through the object volume. The laser light is subjected to forward scattering at the mosquito, and the combined mosquito-object wave and plane reference wave then propagates through free space. This combined wave is focused through a focusing optic (FO) and imaging optic (IO) in a two-component telecentric system onto a sensor (CCD), where the interference pattern is recorded as a digital hologram. A schematic of the collimated cylindrical probe volume and telecentric demagnification system is shown in Fig. 11.
Fig. 11 Experimental setup for optical recording of a digital in-line hologram with a demagnifying two-lens telecentric system. CO: collimating optic, FO: focusing optic, IO: imaging optic, CCD: sensor array.
In the large-scale experiment (see Large Field of View Mosquito Reconstructions), the collimating optic (CO) and focusing optic (FO) were 355 mm diameter off-axis parabolic mirrors with a focal length of 2540 mm, set up in a Z-type interferometer configuration. The imaging optic was a 25.4 mm diameter plano-convex lens with a focal length of 175 mm, providing a demagnification factor (
$ M_D $ ) of 14.53 × and an effective pixel size of 79.93 µm in the recording volume. The sensor was a Ximea CB120RG-CM 4096 × 3072 pixel camera with pixel size of 5.5 µm.For the bednet validation experiments (see Mosquitoes Obscured by a Bednet), the collimating optic was a 25.4 mm plano-convex lens with a focal length of 500 mm, and the two-component telecentric system consisted of 25.4 mm plano-convex lenses with 500 mm and 50 mm, 400 mm and 30 mm, and 500 mm and 30 mm focal lengths to yield effective pixel sizes of 58.60 µm (
$ M_D=10.00\;\times $ ), 78.13 µm ($ M_D=13.33\;\times $ ), and 97.67 µm ($ M_D=16.67\;\times $ ), respectively. These EPS values were chosen based on the results shown in Fig. 1 and previously conducted work28. The sensor was a Dalsa Genie Nano M1920 1936 × 1216 camera with a pixel size of 5.86 µm. These validation experiments were conducted before access to the OAP mirrors was possible, and are included to provide proof-of-concept physical data of the obscured-mosquito localisation techniques at a comparable EPS to the larger field-of-view experiments in Large Field of View Mosquito Reconstructions. This smaller system can be scaled to a larger recording volume by increasing the number of pixels on the sensor and using larger collimating and focusing optics, while maintaining the effective pixel size, wavelength, and object size. -
To assess the noise levels in the background images, the first 100 frames of data were assessed from the 12-bit Ximea recordings with a time stationary scene. The mean intensity across the frames was 1865 with a spatial standard deviation of 255 gray levels. However, with background subtraction, the standard deviation decreased to 80 grey levels. Methods to reduce this speckle such as using a shorter coherence length light source to reduce multiple reflections and scattering between the two panes of glass in the flight chamber will be the subject of further study. The number of pixels above 80% of the saturation (i.e. 80% of 4095) and below 20% are 1 and 1182, respectively (out of 9 million), meaning that the assumption that the recording is within the linear range of the CCD/CMOS array is valid. When a mosquito is introduced, these numbers are 1 and 3782, respectively, due to the mosquito blocking out some of the light, and hence the larger number of dark pixels. Along the time-axis of the first 100 images, the pixel-to-pixel standard deviation, for a random sample of 5 pixels, is 17.51, 6.46, 14.20, 14.22 and 21.16 grey levels, yielding a noise level of 1.2% for the standard deviation of 21.16 compared to the same pixel's mean intensity.
Fig. 12 shows a typical cross-section of a mosquito signal after a background subtraction. The grey level minimum of the mosquito signal is −1621 with diffraction patterns giving local minima at −913 and −596 visible on the left hand side, significantly above the temporal noise level of approx 20 grey levels and spatial noise level of approx 80 grey levels.
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Bednets are composed of nylon fibres, which have an index of refraction of n = 1.5 and an approximate diameter of 100 µm (or approximately 125λ at 785 nm), which are twisted into threads of approximately 4-5 fibres each. The threads are woven into a regular net with an aperture size of approximately 2.5 mm (approx. 3000λ). The aperture size is set to block passage of mosquitoes whilst allowing flow of air to the occupants. The nylon fibres are optically opaque and hence the optical field after transmission is governed by the components passing through the apertures in the net structure. Hence the bednet can be defined as a transmission function where
$ T_B (x,y)=0 $ for all locations B corresponding to the nylon fibres and$ T(x,y)=1 \; \forall \; (x,y) \notin B $ . Similarly, the mosquito can be considered as a transmission function$ T_M (x,y)=0 $ for all points M corresponding to the mosquito and$ T(x,y)=1 \; \forall \; (x,y) \notin M $ . The validity of these assumptions is supported by the comparisons between experimental and synthetic data used to evaluate the performance of the focus metric algorithms and in which the optical fields are manipulated by the aforementioned transmission functions.The smallest feature of interest in the physical experiments are the legs of a mosquito, which have a diameter of 80 µm (or 100λ at 785 nm)38. The forward scattering numerical aperture is given by
$ \theta=1.22\lambda/d $ , where λ is the wavelength, and d is the diameter of the object. This yields a forward scattering numerical aperture of$ {\rm{NA}}\sim0.012 $ . The much larger numerical aperture of the off-axis parabolic mirrors ($ {\rm{NA}}\sim0.07 $ ) means that the full scattering angle is captured, and the most relevant limiter of the optical system performance in this paper is the effective pixel size, which is a direct result of the discretised sampling of a diffraction pattern on a digital CCD/CMOS sensor. -
The reconstruction of a scene from a digitally recorded hologram requires the calculation of the resultant reconstruction images by applying the discrete propagation formulae between multiple planes in small increments (
$ z_{inc} $ ) away from the hologram. The degree of focus of a reconstructed scene is highest at the z-axis position of the axial object location at the time of recording. The 3D position of the object can therefore be determined from a single hologram. -
Reconstruction using the recorded digital holograms was achieved by performing a two-step thin-lens fourier transform operation to simulate propagation through the two-component telecentric system in reverse, with specific focal lengths according to the optics used to record the hologram. Back-propagation into the object space was performed using a Fresnel transfer function method39. The scene was reconstructed on multiple planes with a z-axis increment of
$ z_{inc}=2 $ mm and focus metrics were calculated for each mosquito found in a reconstructed plane. -
For a non-obscured free-flying mosquito, a simple thresholding technique can be used to identify the XY position of mosquitoes from a hologram. The hologram is thresholded to reveal distinctly bounded areas from the diffraction patterns of forward scattered objects, where the centre of mass of each area is the XY position of a mosquito.
However, for a scene involving a mosquito behind a bednet, additional image processing techniques are used to extract the lateral object position(s). In this case, a two-pass cascade-correlation technique is used. To explain the cross-correlation process, two intensity images need to be defined: a cropped mosquito-only mask,
$ I_M $ , (shown by the dashed line in Fig. 13a); and a combined mosquito and bednet recorded hologram,$ I_{M,B} $ (Fig. 13b). The first step is that$ I_M $ is cross-correlated against$ I_{M,B} $ , shown by:Fig. 13 a Mosquito-only hologram (mask outlined). b Mosquito-bednet hologram of mosquitoes 40 mm (left) and
$ 55 $ mm (right) behind a bednet at$ z=1.40 $ m.$$ C_1 = I_M*I_{M,B} $$ (1) Where
$ C_1 $ is the first-pass cross-correlation map shown in Fig. 14a. The primary peak in this cross-correlation map indicates the XY position of the mosquito, although several smaller peaks exist due to the holes in the bednet. Thresholding of the cross correlation map removes these smaller peaks, resulting in a thresholded map$ C_{1,t} $ . A threshold value of 0.18 was adequate to remove these smaller peaks without removing the primary peak. This threshold was found by cross-correlating the mask,$ I_M $ , with a bednet-only hologram,$ I_B $ , and the peak of this correlation map was found. The mask selection, in terms of mosquito orientation and distance from the hologram plane, is not as important as maybe expected. For example, for the case of a mosquito placed 100 mm behind a bednet positioned at$ z = 900 $ mm, a mask from a mosquito 1400 mm away from the hologram plane is more similar to the mosquito behind the bednet ($ z=1000 $ mm) than the bednet itself ($ z = 900 $ mm). The absolute similarity between the mask and target is not as important as the difference in correlation between the bednet and the mosquito - the cross-correlation peak indicating the mosquito position can be isolated from the background correlation map, especially after thresholding. Therefore, this mask can also be created using a simulated mosquito-only hologram or a pre-recorded reconstruction of an object of a similar size to a mosquito recorded at the same EPS and with the same incremental distance between reconstructed z-planes. To improve contrast and further refine the lateral position, a secondary mask is formed by an auto-correlation of$ I_M $ , such that:Fig. 14 a First-pass cross-correlation between mask and mosquito-bednet hologram. b Second-pass cross-correlation map, indicating the mosquito XY positions.
$$ I_{M2} = I_M*I_M $$ (2) This step calculates a 2D gaussian function using the original mask, and this secondary mask is cross-correlated against the thresholded first-pass cross correlation by:
$$ C_2 = I_{M2}*C_{1,t} $$ (3) where C2 is the second-pass cross correlation map as shown in Fig. 14b. This correlation map indicates the position of two mosquitoes behind the bednet. Intuitively, the easier to spot mosquito in Fig. 13b corresponds to a stronger cross-correlation in Fig. 14b.
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The peak of a focus metric determines the Z-axis position of a reconstructed object. Previous work indicates that the proposed particle signature function focus metric25, 28 works well for resolving multiple objects, as shown in Effect of Imaging Resolution on Localisation Accuracy, but is less effective in the case of a mosquito obscured by a bednet due to the disturbed reference wave diffracting through the lattice-structure. Fig. 15a, below, shows the focus metric curves of a dead anopheles gambiae mosquito placed
$ z=55 $ mm behind a bednet positioned at$ z=1.40 $ m (mosquito on the right in Fig. 13b). Examining the edge-gradient and Tamura-of-Intensity focus metric curves reveals that these methods are less susceptible to the phase profile created by the disturbed reference wave through the lattice-structured bednet and that the ToI focus metric has two maxima in the approximate z-axis positions of the bednet and mosquito. The phase-based particle signature function focus metric curve contains additional peaks which give false-positive mosquito positions.Fig. 15 a Focus metric curves from reconstruction of a mosquito-bednet hologram (net at
$ z=1.40 $ m, mosquito at 1.455 m), and b bednet-only and mosquito-only holograms.Fig. 15b shows the focus metric curves obtained via reconstruction of a bednet-only hologram (Net) and mosquito-only hologram (Mos), where all three focus metrics localise the bednet and mosquito z-axis positions, but only the data for the ToI metric is displayed. Comparing this to Fig. 15a, it is apparent that the mosquito-bednet graph appears to resemble a superposition of the two separate curves in the ToI and edge-gradient based focus metrics. The later method proposed in Alternative Method: Cascade-Correlation ofFocus Metric (CCoFM) aims to resolve these combined curves as they merge into a single elongated peak at lower z-axis separations between the bednet and mosquito.
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Simulations were used in Mosquitoes Obscured by a Bednet to determine the limits of the proposed methods. Simulated holograms were created by taking in-focus images of a mosquito and bednet separately. The images were both binarised, and the mosquito image was forward propagated using a Fresnel Transfer Function39 up to the position of the bednet (for any desired mosquito-bednet separation). The resultant complex hologram was multiplied by the binarised bednet image to simulate the strands of the bednet (as 0 intensity) blocking some parts of the forward propagating light. This combined image was then propagated the desired distance to the back focal plane of a two-component telecentric system. A pair of fourier transform operations simulated propagation through the system and onto a CCD. The image was then resized onto the correct number of pixels as required by the demagnification factor, and the absolute value of each pixel was determined to simulate intensity data (rather than complex-valued amplitude-phase data). The intensity was remapped in integer values [0 4095] to simulate a 12-bit recording device. For back-propagation and object reconstruction, the same process was used as for the physical data.
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The CCoFM follows a similar methodology as the XY localisation technique described in XY Localisation. First, a mosquito-only focus metric mask,
$ F_M $ , is defined by cropping a Tamura of Intensity focus curve from the reconstruction of a mosquito-only hologram at the dashed lines shown in Fig. 16a. This mask can also be obtained from simulated data of an object of similar size, or from a mosquito positioned in a different z-axis position. An important point to note on mask selection is that the z-axis reconstruction increment ($ z_{inc} $ ) and effective pixel size ($ \Delta{x}_e $ ) must be the same for both the mask and reconstruction of interest, and the mask should be appropriately symmetrical. A combined mosquito and bednet focus metric,$ F_{M,B} $ , as shown in Fig. 16b, appears to be the superposition of the bednet-only focus metric and mosquito-only focus metric shown in Fig. 16a. Cross correlating$ F_M $ and$ F_{M,B} $ yields the cross correlation map$ F_{C1} $ :Fig. 16 Tamura-of-Intensity focus metric vs z-axis reconstruction distance: a separate single object curves of mosquito and bednet; b obtained curve of mosquito behind bednet; c cross-correlation curves demonstrating improved z-axis localisation and separation of the two objects.
$$ F_{C1} = F_M*F_{M,B} $$ (4) This cross-correlation map is then thresholded to retain values > 0.4 as shown by CCM1 in Fig. 16c and assigned as
$ F_{C1,t} $ . An autocorrelation of the mask$ F_M $ yields a secondary mask,$ F_{M2} $ :$$ F_{M2} = F_M*F_M $$ (5) The secondary mask,
$ F_{M2} $ , is cross-correlated against the thresholded first-pass cross correlation map$ F_{C1,t} $ to yield a final cross-correlation map,$ F_{C2} $ , with two well-separated maxima indicating the bednet and mosquito z-axis positions as shown by CCM2 in Fig. 16c.
The application of digital holography for accurate three-dimensional localisation of mosquito-bednet interaction
- Light: Advanced Manufacturing 3, Article number: (2022)
- Received: 28 October 2021
- Revised: 23 February 2022
- Accepted: 24 February 2022 Published online: 09 June 2022
doi: https://doi.org/10.37188/lam.2022.020
Abstract: Understanding mosquito interaction with long-lasting insecticidal bednets is crucial in the development of more effective intervention methods to protect humans from malaria transmission. As such, a 240 × 240 × 1000 mm laboratory setup for the in-line recording of digital holograms and subsequent in-focus reconstruction and 3D localisation of mosquitoes is presented. Simple bednet background removal methods are used to accurately localise a mosquito obscured by a bednet in 3D coordinates. Simulations and physical data demonstrate that this method is suitable for mosquitoes positioned 3−1000 mm behind a bednet. A novel post-processing technique, involving a cascade-correlation of a Tamura of Intensity focus metric extracted from digitally reconstructed scenes, accurately localises mosquitoes positioned 35−100 mm behind a bednet from a single digital hologram. The result of this study is a scalable digital holographic methodology to examine mosquito-bednet interaction in 3D at a level of accuracy previously only seen in 2D imaging of mosquitoes in a much smaller volume.
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