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Abstract
Laser speckle contrast imaging (LSCI) is a non-invasive and affordable technique to visualize skin perfusion. Handheld use of the system facilitates measurements on various skin areas in a flexible manner. However, movement artefacts caused by handheld operation or test subject movements hamper its performance. In this work, we study the influence of the laser beam type in handheld-LSCI by evaluating the speckle contrast on static objects for beams with planar, spherical or scrambled wavefronts, and for movement artefacts caused by tilting or translation of wavefronts. We show that the scrambled waves made by often-used engineered diffusers lead to significantly larger movement artefacts than planar or spherical waves.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Laser speckle contrast imaging (LSCI) is a well-known technique to study cutaneous blood flow [1]. The skin is illuminated with coherent light and the backscattered light forms a so-called speckle pattern on the imaging sensor array. Due to the interaction of light with moving red blood cells (RBCs) within the capillaries, the speckle patterns become time dependent. Different flows of RBCs will cause different blurring levels of the time integrated speckle patterns. The parameter speckle contrast is used to evaluate the actual flow [2–5]. The sensitivity of speckle patterns to small movements necessitates that during the measurement, no other source of movements should exist in order to form a reliable perfusion map. Therefore, practical realization of such experimental environment remains a challenge.
Some applications of LSCI include dermatology, burns and the diabetic foot [6,7]. It would be ideal to have a compact and handheld LSCI in order to operate measurements on various patient body areas without inconvenience for patients or investigators [8]. From one side, patient movements originated by breathing, heartbeat and organ tremor is a source of movement artefacts [9,10]. From another side, when using handheld, operator-generated movements of the LSCI system caused by the operator are another source of movement artefacts. Several approaches have been proposed for decreasing movement artefacts. To measure movement related signals (i.e. speckle contrast or perfusion unit) opaque static objects have been placed in the imaging field-of-view (FOV) [11–13]. In this way, the measured signal generated by the object is only influenced by the applied handheld movements, which enables identification and potentially removal of these artefacts. It has been shown that using a motorized gimbal stabilizer, handheld-LSCI can be realized which is less influenced by movement artefacts [14]. To obtain a less noisy perfusion map, multiple perfusion maps are temporally averaged. In handheld measurements, these perfusion maps are often co-registered by segmentation or edge detection of natural textures of samples [15] or the static objects within the FOV.
As the quality of the illumination and the imaging systems directly influences the quality of LSCI measurements, the influence of the spectral width of the light source on the speckle contrast has been investigated [16]. A yet unexplored issue is the influence of the way in which the laser beam is formed. In this work, we focus on the wavefront types in the illumination system and study the speckle contrast during motorized and handheld measurements on static objects. We consider several types of movements and explore the difference between using planar, spherical and scrambled waves. We also examine whether the incorporation of an aiming beam in the handheld system will help investigators to keep the system more stable during handheld measurements. The dataset for motorized and handheld measurements can be found in Dataset 1 [17].
2. Methods and materials
2.1 Handheld LSCI system
A continuous wave single longitudinal mode laser (CNI MSL-FN-671) of ${\rm 671}\pm 1$ nm wavelength with the output power of ${\rm 300}$ mW and a coherence length of longer than ${\rm 50}$ m was chosen as the light source. Its output light was directed through an absorptive filter with optical density of $0.2$ (Thorlabs NE02A) which was placed non-perpendicularly to the beam to prevent direct reflection to the laser tube. Broadband dielectric mirrors of wavelength ${\rm 400}-750$ nm (Thorlabs BB1-E02) were used to direct the laser beam into a microscope objective of magnification $20$ (Nikon CFI Plan Fluor DIC N2) mounted on a three axis stage (Thorlabs Nanomax 300) in order to focus the light into a single mode fiber (Thorlabs SM600) with operating wavelength of ${\rm 633}-780$ nm and a cladding diameter of $125\rm ~micron$. The distal end of the fiber was mounted on the probe. The choice of the single mode fiber was to prevent speckle change due to the movements of handheld-LSCI probe. A monochrome camera (${\rm Basler}~acA2040~55um~USB3$) was mounted on the probe to record the speckle intensity maps with a frame rate of ${\rm 40}$ Hz, exposure time of ${\rm 10}$ ms, imaging depth of ${\rm 8}$ bits, pixel size of ${\rm 3}.45~\mathrm{\mu}\textrm{m} \times 3.45~\mathrm{\mu}\textrm{m}$ and frame size of ${\rm 2048}~\textrm{px} \times 1536~\textrm{px}$. The distance from the camera detector array to the object surfaces was set to $20\rm \textrm{cm}$ (camera gain of ${\rm 0}~\textrm{dB}$) for motorized measurements and $30\rm ~\textrm{cm}$ (camera gain of ${\rm 9}~\textrm{dB}$) for handheld measurements, respectively. The distances varied slightly during motorized-rotational and handheld measurements.
Figure 1 illustrates the handheld LSCI probe which has a total weight of approximately ${\rm 750}~\textrm{g}$ including the connecting cables and optical fiber. The camera objective (FUJINON HF16XA-5M) had a ${\rm 16}~\textrm{mm}$ focal length and based on prior measurements on our imaging geometry, the ${\rm f}-number$ was set to $F8$ to obtain the optimum point for (1) the speckle size to meet the Nyquist criterion [18] and (2) the detected light intensity to have the required dynamic range for computation of speckle contrast. With a distance of ${\rm 20}~\textrm{cm}$ from the camera sensor array to the object surface, the measured resolution was ${\rm 26}.8~\textrm{px/mm}$; hence, the total field-of-view was ${\rm 7}.6~\textrm{cm}\times 5.7~\textrm{cm}$. A hard coated bandpass interference filter of wavelength ${\rm 675}\pm 12.5~\textrm{nm}$ (Edmund Optics) was mounted on the camera objective in order to reduce the background light although the general lighting of the laboratory were turned off during the experiments. To avoid detection of specular reflection from the samples and increase speckle contrast, a linear polarizer optimized for the wavelengths $\rm ~600-1100~\textrm{nm}$ (Thorlabs LPNIRE 100-B) was used in the imaging system with the polarization direction perpendicular to the polarization direction of the laser beam. Note that the output laser beam was linearly polarized and the polarization was partly lost in the single mode optical fibre. To prevent saturating some areas of the camera, for each scattering medium and for each wavefront type, the laser light intensity coupled to the optical fibre was adjusted by displacing the three axis stage on which the optical fiber tip was mounted. The average values of the recorded speckle intensity maps were in the range of $15-25$ out of $255$. The relatively low average intensity is due to the use of a single mode optical fiber and its maximum tolerable optical power. This was compensated by adding camera gain while making sure that the speckle contrast stays just below unity when a static sample was imaged and the system was mounted. In previous experiments on the used camera, we confirmed that a gain level of $9~\textrm{dB}$ with an average speckle intensity of $15-25$ out of $255$ does not have a significant impact on the measured speckle contrast. This is due to the high signal-to-noise ratio of the camera ($40.2\rm ~dB$). Another limiting factor for further increasing average intensity is to prevent saturation at any camera pixel. This average intensity level makes the speckle contrast to fall on the interval $[0.14,1]$ thanks to the rather high quantum efficiency of the used camera ($70\%$).
Fig. 1. Experimental setup for the handheld measurements. 1: Handheld LSCI system; 2: Delrin plate; 3: Mount platform for the baseline measurements.
2.1.1 Spherical waves
The optical fiber emitted a diverging beam with a nominal numerical aperture of $0.12$ such that the $1/e^2$ beam width at the measurement distance of $20\rm ~\textrm{cm}$ from the fiber tip to the object surfaces was $3\rm ~\textrm{cm}$. The processing window sizes (almost in the center of the array) were ${\rm 150}~\textrm{px}\times 150~\textrm{px}$ except for handheld measurements on the custom-made phantom which was ${\rm 120}~\textrm{px}\times 120~\textrm{px}$.
2.1.2 Scrambled waves
To create a scrambled beam, a $20^\circ$ top hat engineered diffuser (Thorlabs ED1-S20-MD) with square scattered shape was mounted at a distance $32.4\rm ~\textrm{mm}$ from the fiber tip. This created a square of width $7.8\rm ~\textrm{cm}$ on the object surface for the motorized measurements. The window size to process speckle intensity frames for scrambled waves was set to ${\rm 150}~\textrm{px}\times 150~\textrm{px}$.
2.1.3 Planar waves
A parallel beam of diameter $2.5\rm ~\textrm{cm}$ with planar wavefronts was created by collimating the laser beam with a pair of plano-convex (Thorlabs LA1608) and bi-convex (Thorlabs LB1945-A-ML) lenses. The distance from the fiber tip to the front side of the bi-convex lens was set to $65.5\rm ~\textrm{mm}$. For this wavefront type in motorized measurements, the maximum possible window sizes to process speckle intensity maps were ${\rm 55}~\textrm{px}\times 55~\textrm{px}$, ${\rm 70}~\textrm{px}\times 70~\textrm{px}$, ${\rm 115}~\textrm{px}\times 115~\textrm{px}$ and ${\rm 120}~\textrm{px}\times 120~\textrm{px}$ for rotational movements on Delrin, rotational movements on matte, object rotation on Delrin and object rotation on matte, respectively. It was ${\rm 150}~\textrm{px}\times 150~\textrm{px}$ for the translational movements. In the handheld measurements, they were ${\rm 75}~\textrm{px}\times 75~\textrm{px}$, ${\rm 65}~\textrm{px}\times 65~\textrm{px}$ and ${\rm 65}~\textrm{px}\times 65~\textrm{px}$ on Delrin, custom-made phantom and matte, respectively.
2.1.4 Aiming beam
A laser source (RGB Laser Systems Minilas) of wavelength ${\rm 660}~\textrm{nm}$ was mounted on the handheld probe to be used as a guide for some of the handheld measurements where its beam was projected on a cross target shown in Fig. S1.
2.2 Controlled movements on motorized stages
The experimental plan for the motorized measurements is illustrated in Fig. 2. Three types of wavefronts, namely spherical, planar and scrambled were included in the experiments. From the sample side, three types of media, namely a metal plate painted with color white matte, Delrin and phantom (to be specified later) were used for the measurements. For the motion mimicking schemes, translational movements parallel to the medium’s surface were applied to study the effect of translation of wavefronts; tilt movements were applied to generate tilt of wavefronts; and rotational movements were applied to realize a combination of the first two which is a form of movements occurring during a handheld operation. Note that translation of the system towards the medium’s surface is considered negligible due to its small effect on the speckle intensity map. Also, compared to the other types of motion, rotation around the optical axis will be small during a typical handheld operation.
2.2.1 Translation
The handheld probe (facing to the static objects) was mounted on a linear translational stage (Zaber X-LHM200A-E03) with the travel length of ${\rm 20}~\textrm{cm}$, speed range of ${\rm 0}-6.5~\textrm{cm/s}$ and speed resolution of ${\rm 76}~\textrm{nm/s}$. Here the probe moved parallel to the object surface as animated in Visualization 2.
Fig. 2. Schematic diagram of the experimental setup for the motorized measurements. For rotational motions, translational motions and wavefront tilting see Visualization 1, Visualization 2 and Visualization 3, respectively. The centers of rotation for system rotation and wavefront tilting are indicated by the green and black dots, respectively.
2.2.2 Rotation
A high precision rotation mount (Thorlabs PRM1/M28) with the angular speed range of ${\rm 0}-25~^\circ\textrm{/s}$ and minimum step size of ${\rm 25}~\textrm{arcsecond}$ was employed to apply rotations. For the rotational movement, the rotation mount was placed between the handheld probe and a fixed vertical bar attached to the optical table such that the green point on the fiber tip became the center of rotation (see Visualization 1). For the tilt movement, this rotation mount was attached to the static medium while the handheld probe facing the medium at the distance of ${\rm 20}~\textrm{cm}$ (from the camera sensor array to the object surface) was fixated on the optical table such that the black point on the object surface and just in front of the fiber tip became the center of rotation (see Visualization 3). The controller for this stage was a brushed DC servo motor unit (Thorlabs KDC101). The speed profiles were applied to the motor unit using the software Kinesis.
2.3 Static phantoms
Three scattering media were used in this study. The first medium was a wide plate of thickness ${\rm 10}.9~\textrm{mm}$ made of Polyoxymethylene material (Delrin). The second sample, referred to as matte, was a metal plate painted ${\rm 6}~\textrm{times}$ with spray paint of color white matte (Ecopaint Vintage chalk paint spray 400 ml). This medium has a very high scattering level; thus, only surface scattering occurs. The third medium was a tissue mimicking scattering phantom of reduced scattering coefficient ${\rm 2}~\textrm{mm}^{-1}$ and absorption coefficient ${\rm 0}.01~\textrm{mm}^{-1}$. These optical properties for our operating wavelength of $671~{\rm nm}$ were adapted from Lister et al. [19]. Agar powder (Sigma A7921-500G) was used to make the phantom relatively static and reduce the Brownian motions. A stock solution of demi-water at boiling temperature with $2\%$ agar was prepared. To control the absorption level of the phantom, the Ecoline 700 ink (Talens) was added when the stock solution had cooled down to around ${\rm 60}~^\circ\textrm{C}$. Using the spectrophotometer of wavelength $\rm [300-1100~\textrm{nm}]$ (Shimadzu UV-2600) the absorption coefficient of Ecoline at $671~{\rm nm}$ was measured as ${\rm 24}.6~\textrm{mm}^{-1}$. Then, for making the phantom optically scattering, Intralipid $20\%$ (Fresenius Kabi Nederland BV) assuming the reduced scattering coefficient of ${\rm 26}~\textrm{mm}^{-1}$ [20], was poured to make ${\rm 7}.7~\textrm{vol}\%$. The prepared solution was cast in a 3D printed mold of Polylactic Acid (PLA) material with the effective dimension of $140\times 140\times 14.1\rm ~\textrm{mm}^3$ and was kept for two hours to reach the room temperature.
2.3.1 In-vivo measurements
Two healthy male subjects were involved in in-vivo experiments. Translation of the LSCI system as explained in Section 2.2.1 was applied to forearm of the test subjects who were sitting in a comfortable position during the experiments. Subjects were asked to refrain from intensive physical activity at least 30 minutes before start of the experiments.
2.4 Data analysis
The total acquired speckle intensity frames for translational movements, rotational movements, object rotation and handheld operations were $800$, $1000$, $1000$ and $2400$, respectively. The contrast of the region-of-interest (ROI) within each frame was calculated as [21];
where $\sigma _I$ and $\bar {I}$ indicate the standard deviation and the mean of pixel values within each frame. In this way, a speckle contrast vector including the baseline and the actual measurement was computed per experiment. The equation for speckle contrast drop percentages shown in Tables 1,2, S1, and Fig. 4(c) is; where $C_0$ and $C_1$ are speckle contrasts at speed zero and speed of interest, respectively, for the motorized experiments; and the average speckle contrast for baseline and handheld, respectively, for the handheld experiments.
Table 1. Speckle contrast drop percentages from the maximum values at zero speed to rotational speed of ${\rm 1}.1~^\circ\textrm{/s}$, translational speed of ${\rm 0}.6~\textrm{cm/s}$ and tilt speed of ${\rm 1}.1~^\circ\textrm{/s}$ measured on Delrin and matte. Based on our previous study [22], these are averaged values of a number of handheld measurements employing an EM-tracking system. Data are extracted from Fig. 3.
Table 2. Speckle contrast drop percentages from the averaged values at baselines to the averaged values of the associated handheld measurements shown in Fig. 5. Avg.: Averaged.
2.4.1 Speckle contrast window size
In order to achieve an appropriate statistics, we used a rather larger ROI (above ${\rm 50}\times 50~\textrm{px}$) for the calculation of the speckle contrast than what is normally used (below ${\rm 10}\times 10~\textrm{px}$) when imaging a tissue subject. We realized that a large ROI may give wrong result if an intensity gradient exists within the ROI. Then, we checked this not to be the case by reanalyzing the data with a window size of ${\rm 7}\times 7~\textrm{px}$ at different areas within the ROIs. Also, the variation in the window sizes does not have a significant impact on the observed difference in speckle contrast of the wavefront types at each applied speed. In this regard, we compared graphs of speckle contrast versus translational speed (calculated by both window sizes of ${\rm 70}\times 70~\textrm{px}$ and ${\rm 7}\times 7~\textrm{px}$) for the case of Delrin and matte (See Fig. S3). While a too small ROI may cause a graph with high random variations, a too large ROI may include artefacts such as reflection. Therefore, an optimized window size is chosen according to the type of movement and illumination to ensure that a uniform speckle pattern is used for the calculation of contrast.
2.5 Handheld measurement protocol
Six and 9 healthy volunteers with normal hand tremor participated in the experiments with various beams and with the aiming beam, respectively. Subjects were asked to avoid over-concentration during the handheld measurements since the purpose was to realize movements of the LSCI system during normal handheld operations. During the first ${\rm 10}~\textrm{s}$ of the image acquisition, the handheld LSCI system was mounted on the rest position to make a baseline measurement. Then, it was lifted slowly and kept still by subjects standing normal in front of the setup and with arm bent at elbow at ${\rm 90}^\circ$ for a ${\rm 40~s}$ handheld measurement (Fig. 1). The distance from the camera sensor array to the imaged object was almost ${\rm 30}~\textrm{cm}$. The measurements were carried out on 3 scattering media ($3$ series) each with 3 beam types to obtain the average speckle contrast. In each series, 6 test subjects participated and to prevent the issue of fatigue, a gap of at least 45 minutes between measurements was considered for each test subject. The same experiment protocol was followed for the experiments of aiming beam where $9$ test subjects were included in the study.
3. Results
3.1 Motorized measurements
First, the LSCI system was rotated from an angle normal to the object surface to the angle of ${\rm 22}.5^\circ$ with an acceleration of ${\rm 0}.2~^\circ\textrm{/s}^2$ in ${\rm 15}~\textrm{seconds}$ time. The same angular speed was applied for spherical, planar and scrambled beam types. The speckle contrast vs. the applied rotational speed is depicted in Fig. 3(a), 3(d), for Delrin and matte, respectively. The drop in speckle contrast is smallest for the spherical wavefront and largest for the scrambled wavefront, and for these beams the contrast drops are quite similar for both media. The behavior for the planar waves is in between those of the other beam types, with a larger sensitivity for Delrin than for matte.
Fig. 3. Motorized movements of the LSCI system (a-c) on a Delrin plate and (d-f) on a matte surface for spherical, planar and scrambled wavefronts. Speckle contrast vs (a,d) rotational and (b,e) translational speeds. (c,f) Speckle contrast versus applied tilt speed realized by object rotation. For spherical, planar and scrambled wavefronts see Visualization 4, Visualization 5 and Visualization 6, respectively, where translational motions are applied on a Delrin plate. For rotational motions and object rotation see Visualization 7 and Visualization 8, respectively, where a Delrin plate and spherical wavefronts are employed. Solid curves: second order exponential fit functions.
Second, translational displacement of the system over ${\rm 8}.7~\textrm{cm}$ in ${\rm 5}.8~\textrm{seconds}$ time with an acceleration of ${\rm 5}.2~\textrm{mm/s}^2$ was applied. See Fig. 3(b), 3(e), for the Delrin and matte objects, respectively. Visual comparisons of speckle intensity maps and the corresponding speckle contrast vs applied translational speed on Delrin for spherical, planar and scrambled wavefronts are provided in Visualization 4, Visualization 5 and Visualization 6, respectively. Here the beam with planar wavefronts has the lowest sensitivity to motion and the scrambled beam the highest, and for these beams the contrast drops are quite similar for both media. The spherical wavefronts give a result in between for Delrin, while giving the same contrast vs speed relation as the planar wavefronts for matte.
Third, a tilt of spherical, planar and scrambled wavefronts was realized by rotating the samples with the same angular speed profile as the first series, that is, the acceleration of ${\rm 0}.2~^\circ\textrm{/s}^2$ in ${\rm 15}~\textrm{seconds}$ time. Here the samples started from the angle of ${\rm 25}^\circ$ with respect to the optical fibre axis and traveled an arc of ${\rm 22}.5^\circ$ towards optical fibre axis. Speckle contrast values vs tilt speed for Delrin and matte are shown in Figs. 3(c), 3(f), respectively. For matte there is only a small drop of speckle contrast for all beam types. For Delrin the contrast drops are much larger. For both media, the difference between the three beam types is much smaller for tilt and for translation or rotation. A visual comparison of speckle intensity maps between the three movement types (i.e. rotation, translation and tilt) with the spherical beams on Delrin can be found in Visualization 7, Visualization 4 and Visualization 8, respectively. In general, the scrambled beam shows the largest sensitivity to object motion.
3.1.1 In-vivo validation of translation
LSCI measurements on the forearm of two subjects have been performed as introduced in Section 2.3.1. Figure 4(a), 4(b) show the results of speckle contrast versus translational speed for the three types of wavefronts. The speckle contrast values at zero speed are lower than the case of static objects shown in Fig. 3 which is due to the cutaneous microcirculatory blood flow. The difference in the speckle contrast values at zero speed between the various beam types, especially for subject 1, is larger than in-vitro (Delrin or matte). This can be due to the change in blood flow of the imaged regions. Therefore, in order to perform a fair comparison between the wavefront types, speckle contrast drop percentages introduced in Eq. (2) with $C_0$ and $C_1$ being the speckle contrast values at zero speed and translational speed of ${\rm 0}.6~\textrm{cm/s}$, respectively, have been calculated. As shown in Fig. 4(c), for subject 1, the least speckle contrast drop percentage has been achieved with planar wave ($21.3\%$), compared to spherical wave ($29.9\%$) and scrambled wave ($34.4\%$). Similarly, for subject 2, the least speckle contrast drop percentage has been achieved with planar wave ($18.7\%$), compared to spherical wave ($27.7\%$) and scrambled wave ($30.2\%$). This suggests that plane waves cause the least movement artefacts when the LSCI system is purely translated.
Fig. 4. Motorized translation of the LSCI system on forearm of two healthy subjects. (a-b) Speckle contrast versus translational speed for subjects 1 and 2, respectively. Solid curves: second order exponential fit functions. (c) Speckle contrast drop percentages (introduced in Eq. (2)) from the maximum values at zero speed to the translational speed of ${\rm 0}.6~\textrm{cm/s}$. Based on our previous study [22], the translational speed of ${\rm 0}.6~\textrm{cm/s}$ is the averaged value of a number of handheld measurements employing an EM-tracking system. Data of (c) are extracted from (a-b).
3.2 Handheld measurements
The results of the 3 series of the handheld measurements, namely, on matte, on agar-Intralipid phantom, and on Delrin plate are depicted in Figs. 5(a)–5(c), respectively, where each experiment index per graph refers to an identical test subject. Therefore, the data of $3$ groups of $6$ test subjects are shown. Note that the members of mutual groups are not necessarily the same. To have an outlook on the three series, the data of $6$ experiment indices within each series are averaged (Fig. 5(d)).
Fig. 5. Speckle contrast of handheld measurements on (a) matte, (b) agar-Intralipid phantom and (c) Delrin and for planar, spherical and scrambled wavefronts. (d) Speckle contrast (mean$\pm$standard deviation) for various scattering media and wavefronts.
The last step of the study was devoted to the potential difference an aiming beam might make in terms of speckle contrast during handheld measurements. Therefore, subjects operated handheld measurements on the Delrin plate, with spherical beam and having an aiming beam mounted on the handheld LSCI system. The comparison was made with the data of that of Delrin, with spherical beam and without an aiming beam. The averaged speckle contrast for $9$ test subjects is shown in Fig. S2 where each experiment index refers to an identical test subject and the last column pair shows the average value of the experiment indices.
3.3 Hardware and data analysis considerations
3.3.1 Use of a linear polarizer
As mentioned in Section 2.1, a linear polarizer is mounted on the imaging system. The direction of the polarizer is perpendicular to the direction of the polarization of the light source in order to minimize the artefact caused by specular reflection (see Fig. S4). It is worth noting that the use of a polarizer helps to detect nearly fully developed speckle patterns in case of no movements at the expense of the intensity loss. The underlying reason is filtering the portion of the backscattered light with various polarization directions except that of parallel with the direction of the linear polarizer. Therefore, a higher dynamic range with respect to the speckle contrast is achieved.
3.3.2 Gaussian beam illumination
Apart from the engineered diffusers being compact, they provide a uniform illumination on the target tissue. Since the speckle contrast introduced in Eq. (1) is independent of the intensity level, a uniform illumination is not a requirement for obtaining a valid speckle contrast map from a wide tissue area. Note that in order to minimize the possibility that the speckle contrast is influenced by intensity gradient, (1) the mean intensity should not be so high that parts of the camera sensor is saturated; (2) the mean intensity should not be so low (below $5 \%$ of the maximum observable value) that the camera noise level becomes comparable with the detected intensity level. The laser light after expansion on a tissue surface is of a Gaussian nature. The larger the distance from the center of the beam, the lower the observed intensity. Therefore, as long as the mean intensity falls within the valid range, illuminating a target tissue with spherical wave illumination would not affect the relative speckle contrast at different locations of the illuminated tissue (see Fig. S5).
4. Discussion
In this work, we focused on illumination schemes for handheld LSCI and their influence on the movement artefacts studied by measuring speckle contrast during motorized and human handheld measurements on the extreme cases of high scattering (matte) and low scattering (Delrin plate) and on a tissue mimicking phantom. To exclude any other source of movements than the LSCI system, experiments were carried out on static scattering media. The first phase of the study consisted of applying three motion mimicking methods (i.e. translational, rotational and object rotation) to the system. The results are shown in Fig. 3. It appears that, for each type of applied motion, the relation between the speckle contrast and the amount of applied motion depends on (1) the type of the illuminations and (2) the scattering level of the media. In general, the contrast’s sensitivity to motion increases with decreasing scattering level, and scrambled wavefronts give a higher motion sensitivity than spherical and planar wavefronts. For media with tissue-like scattering properties such as Delrin (Fig. 3(a)–3(c)), planar waves give a lower sensitivity than spherical and scrambled waves.
To address these observations, we take a closer look at the system geometry and use the optical Doppler effect. We regard the tip of the optical fiber as a point source emitting spherical waves. Figure 6(a) shows a snapshot of wavefronts at some distance from the source and the corresponding illuminating wave vectors $\vec{k_i}(x,\!y,\!z)$, where $k=2\pi /\lambda$ is the wave number. Here the distance and the wavelength are considered as $z={\rm 20}~\textrm{cm}$ and $\lambda ={\rm 671}~\textrm{nm}$. For a circle in millimeter scale radius, e.g. $a={\rm 1}~\textrm{mm}$ in the $xy$ plane centered about the $z$ axis, the wavefronts may look curved with the Fresnel number of $F_N=a^2/(\lambda z)=7.4$ which is greater than unity. In other words, within a typical distance over which light diffuses from the point of injection to the point of detection, the wavefront is significantly curved. This contributes to a range of incoming wave vectors when the medium has a low scattering level such as Delrin. In Fig. 6(b), a collimating system is used to create plane waves having a constant wave vector toward the scattering medium. In Fig. 6(c), an engineered diffuser is used to create scrambled waves. In this case, each illuminated point of the diffuser is a point source of light with random phase. As a consequence, each location on the surface of the scattering medium is illuminated by light with a range of wave vectors with a small angular variation.
Fig. 6. Schematic diagram of illumination and imaging systems in a reflection geometry where the scattering medium is illuminated with (a) spherical, (b) planar and (c) scrambled waves. $\vec{k_i}$: incoming wave vectors (normals to the wavefronts) toward the scattering medium; $\vec{k_s}$: outgoing wave vectors from a scattering spot collected by the imaging lens. The half circle with gradient red color represents the fluence distribution of light eventually being imaged on a certain point in the imaging plane. The solid lines within the fluence distribution show random pathways. Green circles on the fiber tips: center point for rotation of the LSCI system in the experiments of rotational displacements; Black circles: center point for rotation of the medium in the experiments of wavefront tilting. Scales are exaggerated for the sake of demonstration.
The light entering the scattering medium travels random pathways and a portion of it called the diffused light comes back to the surface. The fluence distributions shown in Fig. 6 symbolically represent the fluence of light returning to the tissue surface in a point conjugated with a certain position on the imaging plane within a cone defined by the imaging system. The range of wave vectors $\vec{k_s}(x,\!y,\!z)$ of detected light is the same for the three illumination schemes since the imaging geometry remained unchanged. The time scale of intensity fluctuations in the image plane determines the blurring of the time integrated speckle pattern and therefore its contrast. It is the variation of the optical Doppler shifts that determines the time scale of speckle intensity fluctuations (therefore, the blurring level of the time integrated speckle patterns) rather than the absolute values of the optical Doppler shifts. The reason is that intensity fluctuations are the result of interference between light fractions with a different Doppler shift: if all light had the same Doppler shift, there would be no intensity fluctuations.
First we discuss the case of linear translation. If the optical system moves with velocity $\vec {v}$ along the $x$ axis relative to the measured medium, i.e. $\vec {v}=(v_x,\!0,\!0)$, the Doppler shift of light obeys [23]
independent of the details of the light paths inside the medium. A variation of wave vectors $\vec{k_s}$ and $\vec{k_i}$ will cause a range of Doppler shifts leading to intensity fluctuations. The spread of detected wavevectors $\vec{k_s}$ depends only on the lens aperture which is kept unchanged during this study. Assuming a lens aperture opening or closing of $1\rm ~\textrm{mm}$, the maximum two-sided Doppler shift of light per each ${\rm mm/s}$ of translational speed based on Eq. (3) is $7.45\rm ~Hz$, for the wavelength of $671\rm ~\textrm{nm}$ and the distance from the object’s surface to the lens aperture of $20\rm ~\textrm{cm}$. Due to the high scattering properties of matte, only one incoming wave vector $\vec{k_i}$ contributes to the creation of Doppler shift for the planar and spherical waves. This results in the same response to the applied translational speed for the planar and spherical waves (see Fig. 3(e)). Moreover, for the plane waves, there is only one incoming wave vector $\vec{k_i}$ that makes the results for Delrin and matte the same, as shown in Fig. 3(b), 3(e). For the spherical waves, the Doppler shift range will be greater than the plane waves since the scattering spot contains a range of incoming wave vectors (Fig. 3(b)). As an example, consider a scattering spot of radius $a=1~{\rm mm}$. The maximum two-sided Doppler shift of light based on Eq. (3) can be calculated (in Hertz) as $\Delta \nu =2av/(\lambda z)={\rm 14}.9~Hz$ per each ${\rm mm}/s$ of translational speed for the spherical waves at ${\rm \lambda} =671~\textrm{nm}$ and $z=20\rm ~\textrm{cm}$. This maximum frequency exists in the power spectrum of intensity fluctuations observed at the point on the camera sensor conjugated with the points of radius $a={\rm 1}~\textrm{mm}$ located on the medium’s surface. As a consequence, for an exposure time of $10\rm ~ms$, the calculated Doppler shift can be expected to cause a non-negligible speckle contrast drop. Since a range of incoming wave vectors contribute to each location on the scattering spot caused by scrambled waves, the resultant Doppler shift range will be more than that of planar and spherical waves. For the same reason as that for spherical waves, the Doppler shifts will be less in the case of higher scattering medium for the scrambled waves. Finally, the results for the spherical beam is much more medium dependent than for the planar waves and the scrambled waves, as can be seen in Fig. 3(b), 3(e). To examine the reproducibility of the data, this experiment has been carried out again (see Fig. S3(a), S3(b) where the results are in agreement with Fig. 3(b), 3(e). Note that the range of incoming wave vectors $\vec{k_i}$ dictates the phase structure of the incident light on the sample. This phase structure is constant for plane waves. It gradually changes for the spherical waves. And it is randomly distributed for the case of scrambled waves.Rotation of the illumination and imaging systems along the fiber tip (the green point located on the fiber tip shown in Fig. 6) with a certain angular velocity will also cause Doppler shifts. Equation (3) cannot be used with its current form since for rotation the details of the light trajectories will matter. Since the fiber tip is also origin for propagation of spherical waves, the incoming wave vectors tend to match the curve of rotation and since the outgoing wave vectors also rotate in the same direction, the dependence of the Doppler shift on angular speed is minimum for the case of spherical waves. This would not be the case for planar waves since the incoming wave vectors exist in one direction and rotation of the system causes the change in the relative angles of incoming and outgoing wave vectors (Fig. 3(a)). What is more, for the plane waves, these relative angles also depend on the scattering level of the medium. As the scattering spot becomes smaller with higher levels of scattering, the caused Doppler shift range decreases (Fig. 3(d)). However, this is not the case for the spherical and the scrambled waves as they result in the same behavior in the case of matte and Delrin.
Now consider wavefront tilt, generated by rotation of the object along a point on its surface just in front of the fiber tip on the optical axis (the black points shown in Fig. 6). In case of very high scattering and therefore a very small scattering spot, the incoming and outgoing wave vectors come from the same location on the medium’s surface. If this location is close enough to the point of rotation, the effective velocity contributing to the Doppler shift remains zero. In practice, for wavefront tilting we observed relatively low speckle contrast drop for all three illumination schemes for measurements on matte as depicted in Fig. 3(f). The slight decay of all three curves is because the ROI includes the area around the center of rotation. As this ROI increases, we expect more contrast drop. For Delrin, a less scattering medium, the scattering spot will be wider and this results in a larger differences between the incoming and outgoing wave vectors. Furthermore, in Delrin, tilting causes a space dependent velocity component of the tissue towards or away from the LSCI system, causing a rather larger contrast drop for all three beam types (see Fig. 3(c)). To sum up, for all beam types, there is a larger sensitivity to motion for tilt speed for Delrin, and an almost zero sensitivity for matte for tilt speed. A summary of the speckle contrast drops for the motorized measurements depicted in Table 1 suggests that the least speckle contrast drop is achieved by using (1) spherical waves while applying rotations; (2) planar waves while applying translations or tilt. This means that the choice of appropriate illumination potentially controls system sensitivity to the applied movements.
In the handheld measurements, a combination of all of the aforementioned movements takes place. Also, the magnitude of each motion type varies per person as in a previous study [22], we measured an averaged on-surface beam speed and tilt speed of $0.9~{\rm cm/s}$ and $1.1~\rm ^\circ\textrm{/s}$, respectively, for ten healthy operators using an electromagnetic (EM) tracking system. Table 2 summarizes the speckle contrast drop percentages from the baseline to the averaged values shown in Fig. 5. As the medium becomes less scattering, the speckle contrast drop percentages increase (for all beam types). On average, the scrambled waves created by the engineered diffuser cause the lowest speckle contrast (or the greatest speckle contrast drop) in either illumination schemes and in either scattering samples, while the planar wavefronts result in the highest averaged speckle contrast (or the lowest speckle contrast drop). The speckle contrast drop percentages from the averaged baseline to the values of the handheld measurements without and with an aiming beam shown in Fig. S2 are summarized in Table S1. The difference in the speckle contrast drop percentages tend to vary per test subject. For some, using an aiming beam causes less drop percentages while for others the other way round. On average, the results stay close to each other: $43.3\%$ with and $42.6\%$ without using an aiming beam. Therefore, one can conclude that for this group of test subjects while employing spherical illumination, use of an aiming beam does not decrease the movement artefacts.
Nowadays, most of the laser speckle perfusion imaging systems use engineered diffusers because it is an easy method for creating uniform illumination. Here, we have shown that using engineered diffusers is the worst option in terms of movement artefacts, with planar wavefronts being the best option. However, creating a planar beam of large size requires bulky optics. Furthermore, planar and spherical waves make a non-uniform Gaussian-shape light intensity which might affect measurement of speckle contrast at ROIs a couple of centimeters away from the beam center due to a lower average intensity. Results of this study can be used to devise solutions for suppressing movement artefacts in future handheld LSCI systems.
Funding
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (14538).
Acknowledgments
We are grateful to Sjoukje M. Schoustra for designing Fig. 2. We thank all the persons who helped us with the handheld operations. This study was supported by the Open Technology program of the Netherlands Organization for Scientific Research (NWO), Domain Applied and Engineering Sciences, under grant number 14538.
Disclosures
The authors declare that there are not any financial interests related to this article and no potential conflicts of interest to disclose.
Data availability
Data underlying the results presented in this paper are available in Dataset 1 [17].
Supplemental document
See Supplement 1 for supporting content.
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