Prediction of motion artifacts caused by translation in handheld laser speckle contrast imaging

Abstract

Significance: In handheld laser speckle contrast imaging (LSCI), motion artifacts (MA) are inevitable. Suppression of MA leads to a valid and objective assessment of tissue perfusion in a wide range of medical applications including dermatology and burns. Our study shines light on the sources of these artifacts, which have not yet been explored. We propose a model based on optical Doppler effect to predict speckle contrast drop as an indication of MA.

Aim: We aim to theoretically model MA when an LSCI system measuring on static scattering media is subject to translational displacements. We validate the model using both simulation and experiments. This is the crucial first step toward creating robustness against MA.

Approach: Our model calculates optical Doppler shifts in order to predict intensity correlation function and contrast of the time-integrated intensity as functions of applied speed based on illumination and detection wavevectors. To validate the theoretical predictions, computer simulation of the dynamic speckles has been carried out. Then experiments are performed by both high-speed and low-framerate imaging. The employed samples for the experiments are a highly scattering matte surface and a Delrin plate of finite scattering level in which volume scattering occurs.

Results: An agreement has been found between theoretical prediction, simulation, and experimental results of both intensity correlation functions and speckle contrast. Coefficients in the proposed model have been linked to the physical parameters according to the experimental setups.

Conclusions: The proposed model provides a quantitative description of the influence of the types of illumination and media in the creation of MA. The accurate prediction of MA caused by translation based on Doppler shifts makes our model suitable to study the influence of rotation. Also the model can be extended for the case of dynamic media, such as live tissue.

Keywords: Doppler effect; analytical models; biomedical optical imaging; computer simulation; laser speckle contrast imaging; model-driven development; motion artifacts; numerical analysis.

Fig. 1

Schematic diagram of the system model reprinted with permission from Ref. . Linear translation of a solid object along the $x–y$ plane in the $x$ direction. Illumination and detection on a solid object of (a) finite and (b) very high scattering levels. (c) Mapping of the bases of the illumination and detection cones on the object’s surface ($x–y$ plane).

Fig. 2

Density functions for incoming and outgoing wavevectors. $\lambda =671\mathrm{nm}$; $V=5\mathrm{mm}/\mathrm{s}$. (a) Case of a semicircular shape and (b) the associated optical Doppler distribution as a result of convolution of $p_{R_{-i}}$ and $p_{R_s}$. (c) Case of a Gaussian shape and (d) the associated optical Doppler distribution.

Fig. 3

Schematic drawing of the single-lens imaging system. S, scattering medium; A, aperture; L, spherical lens; I, image screen; $z_1$, distance from the scattering medium to the lens; $z_2$, distance from the lens to the image screen; and $a_s$, radius of the aperture opening.

Fig. 4

(a)–(d) Simulation of speckle intensity on the image plane of a single-lens imaging system. The speckle frame size is $90\times 90\mathrm{px}$. Case of (a) no aperture (Video 1, mp4, 9.94 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s1]), a square aperture of (b) $46\times 46\mathrm{px}$ (Video 2, mp4, 9.59 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s2]), (c) $12\times 12\mathrm{px}$ (Video 3, mp4, 8.26 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s3]), and (d) $4\times 4\mathrm{px}$ (Video 4, mp4, 8.54 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s4]). For the sake of simplicity, a square aperture is used instead of a circular aperture. Experimental speckle intensities obtained on (e) a matte surface (Video 5, mp4, 17.5 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s5]) and (f) a Delrin plate (Video 6, mp4, 18.1 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s6]). See Sec. 3.2 for the experimental parameters. In all cases, the applied translational speed is $V=10\mathrm{mm}/\mathrm{s}$.

Fig. 5

Comparison between results of simulated time-varying fully dynamic speckle patterns, experiments and the theory for a high scattering medium (matte). The theoretical curves are obtained by Eqs. (9) and (12) for semicircular and Gaussian wavevector density functions, respectively. Normalized intensity autocorrelations with the (a) semicircular and (b) Gaussian forms of the wavevector density functions. The wavevector density functions for theoretical and simulation data are made by $\{{\chi }_i,{\sigma }_i\}=0$ and $\{{\chi }_s,{\sigma }_s\}=26.5\times {10}^{-4}$ (Video 7 mp4, 2.37 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s7]; Video 8, mp4, 4.26 MB [URL: https://doi.org/10.1117/1.JBO.28.4.046005.s8]).

Fig. 6

Speckle contrast (simulations) versus the applied translational speed. The density functions for the wavevectors are (a) semicircular and (b) Gaussian. $\{{\chi }_i,{\sigma }_i\}=0$ simulates spherical waves on matte and planar waves on both matte and Delrin, whereas $\{{\chi }_i,{\sigma }_i\}>0$ simulates scrambled waves on matte.

Fig. 7

Experimental results of the contrast of the time-integrated speckle intensities versus applied translational speed obtained by (a)–(c) low framerate and (d) high-speed imaging setups. Solid curves with the accompanying data points correspond to theoretical and speckle simulation in all subfigures. Data points with error bars represent mean ± standard deviation.