Influence of biological tissue and spatial correlation on spectral changes of Gaussian-Schell model vortex beam

https://doi.org/10.1016/j.optlaseng.2020.106224Get rights and content

Highlights

  • investigate the spectral shift and spectral jump of vortex beam using contour plots.

  • discuss the effect of biological tissue on spectral changes of vortex beam.

  • analyze the influence of spatial correlation on spectral changes of vortex beam.

Abstract

Based on the extended Huygens-Fresnel principle, the analytical expressions of the spectrum for Gaussian-Schell model vortex beam (GSMVB) propagating in biological tissues have been derived. The effects of the field point position, the species of the biological tissues, spatial correlation of beams on the relative spectral shift of GSMVB passing biological tissues have been investigated using the contour plots. It is shown that the spectral change is somewhat slow on the area near the z-axis, whereas the spectral redshift, blueshift and jump occur at far off-axis range. The stronger biological tissue turbulence can delay spectral jump, extend the space of observing the beam spectral jump, weaken the phenomenon of spectral jump on the propagation. Simultaneously, the results can well verify the scientificity and rationality of selecting the mouse as the experimental objects in biomedical research. The spatial coherence of beams can speed up the spectral change and slow the spectral jump down. Additionally, several physical explanations have been given to the above phenomena.

Introduction

Recently the development and applications of Tissue Optics have been promoted accompanied by the researches on the interaction between laser and biological tissues, even extensive interests have been stimulated in the field of adopting the optical means to biomedical spectrum detection as well as diseases diagnosis and treatment [1], [2], [3], [4], [5], [6]. On the basis of the power spectrum of mammalian tissue reported by Schmitt and Kumar [7], the polarization and coherence of random electromagnetic beams in biological tissue have been studied, and the role of tissue structure in the imaging system resolution has been estimated [8], [9], [10], [11]. The effects of partial coherence and biological tissue parameters on beam transmission have been analyzed, and further the feasibility of evaluating the performance and structure of biological tissue system with the aid of beam spread and average intensity of Gaussian-Schell model beam (GSMB) in biological tissue transmission has been determined [12]. Both the scintillation factor and average intensity of laser propagation in biological tissue have been studied [13]. In 2018 Chen et al. introduced a power spectrum model of the soft biological tissues, studied the influence of inner/outer scales of tissues, refractive index variance as well as the slope of the power spectrum to beam propagating in it, pointed out that the further study of laser propagation in biological tissue is useful to the medical diagnostics and treatment [3]. The effects of the several determining factor, including structural constant of biological turbulence, beam parameters, the topological charge and the transverse coherent lengths, on the normalized average intensity and degree of polarization for partially coherent circular flattened Gaussian vortex beams are analyzed by numerical simulation [14]. The intensity evolution of anomalous hollow vortex beam propagating in biological tissues has been analyzed [15]. The role of the turbulent tissue parameters in improving the fiber coupling efficiency has been studied by proposing a model of the fiber coupling efficiency for a partially coherent collimating laser beam propagating through turbulent biological tissue to fiber [16]. The influence of the fractal dimension, strength coefficient of refractive-index fluctuation, small length-scale factor and characteristic length of heterogeneity to the beam wander and long-term spreading induced by tissue turbulence have been analyzed using Wigner distribution function [5].

It is generally known that the spectrum of the light scattered from a certain medium has inseparable relationship with the incident beam and the scattering medium. Spectral analysis is one of the recommendable methods in scientific research, in which one can obtain some interesting information about structure of a deterministic medium, and can optimize performance of light by appropriately adjusting the related parameters of incident beam [17,18]. In 1986, Wolf pointed out that in free space transmission the spectrum of light kept constant while it satisfies the scaling law, otherwise it will experience the correlation-induced spectral changes [19]. Subsequently, the spectral changes of all kinds of beams propagating through the different systems or medium have been studied. For example, the spectrum of partially coherent light diffracted by an aperture has the diffraction-induced spectral changes [20]. Ji et al. analyzed the spectral change of GSMB in atmospheric turbulence and indicated that its normalized spectrum is the same as that of the normalized source, having nothing to do with the quasihomogeneous source as long as the scaling law is valid [21]. The spectral changes steming from the diffraction by the turbulent atmosphere and the source correlation for rectangular array GSMBs has been discussed [22]. Korotkova et al. revealed the dependence of spectral changes on the slope of the fractal spatial power spectrum [23] and the influence driven by the salinity and temperature variation of the water to the spectral shift and central wavelength for optical stochastic beams propagating in the turbulent ocean [24]. The dependence of the general exponent, the inner and the outer scale of atmospheric turbulence, the general structure constant on the spectral changes of rectangular array GSMB has been studied based on the non-Kolmogorov spectrum, respectively [25]. Within the accuracy of the first-order Born approximation, the relationship between the orientation of scattering particle and the distribution of the relative spectral shift of a light wave scattered from an arbitrarily orientated ellipsoidal particle is investigated [26]; the normalized scattered spectrum shifts of GSM arrays beam scattered on a deterministic medium in the far-zone have been examined numerically [17]; the dependence of the near-zone spectral shift and spectral switch of a zero-order Bessel beam scattered from a spherical particle on the effective size of the scattering potential has been determined by numerical simulations [27]; the influence of the scattering medium's parameters and the source's parameters on the spectral shifts, multiple spectral switches, and evolution of relative spectral shifts for the targeted light wave scattered from a semisoft boundary medium in the far zone have been investigated in detail [28]; the effects of the scattering direction, the properties of the incident vortex beam and the scattering medium on the spectral shift and spectral switch of a polychromatic stochastic electromagnetic vortex beam on scattering from a semisoft boundary medium have been investigated numerically [29]. The dependence of spectral shift on the tissue parameters for GSMB passing biological tissue has been discussed [30]. It is noteworthy that few reports about the spectrum of vortex beams in biological tissues are referred to.

Making use of the derived analytical expressions of the spectrum for GSMVB propagating in biological tissues, the relationship between the relative spectral shift and the several determinant factors have been investigated using some numerical calculations, including the propagation position (off-axis distance and propagation distance), the species of biological tissues and the spatial correlation.

Section snippets

Theoretical model

In the space-frequency domain, the cross-spectral density function of GSMVBs on the source plane (z=0) is expressed as [31]W(0)(s1,s2,z=0,ω)=S(0)[s1xs2x+s1ys2y+isgn(m)s1xs2yisgn(m)s2xs1y]|m|×exp[s12+s22w02]exp[(s1s2)22σ02(ω)], where w0 is the waist width, ω is the frequency, s1 and s2 are the position vectors on the source plane. S(0) and σ0(ω) is the spectrum and spatial correlation length of the source, respectively. Sgn() is the sign function, m is the topological charge and is adopted

Numerical calculation and analysis

It is beneficial to investigate the spectrum characteristics and spectrum change of beams propagating in biological tissues for measuring tissue status quantitatively and qualitatively, visualizing the different diseased tissue, and further identifying the different pathological condition of tissues. The relative spectral shift is defined as δω/ω0=(ωmax0)/ω0, accordingly the dependence of δω/ω0 for GSMVB propagating through biological tissues on the off-axis distance r, the propagation

Conclusions

Using the derived analytical expressions of the spectrum for GSMVB propagating in biological tissues based on the extended Huygens-Fresnel principle, the dependence of the relative spectral shift on the propagation position, the species of the biological tissues, spatial correlation length have been investigated numerically. The spectral change is somewhat slow in the region close to z-axis, it may be attributed that the source-induced spectral shift alleviates the effect of biological tissue

CRediT authorship contribution statement

Meiling Duan: Conceptualization, Methodology, Software, Formal analysis, Writing - review & editing, Investigation. Yannan Tian: Data curation, Software, Writing - original draft. Yongmei Zhang: Software, Validation. Jinhong Li: Software, Methodology, Supervision, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the Applied Basic Research Foundation of Shanxi Province, China (Grant Nos. 201701D121011, 201801D221153, 201801D121149), the Outstanding Young Scholars of Shanxi Province, China (Grant No. 201801D211006), and the Fund for Shanxi “1331 Project” key Innovative Research Team (1331KIRT).

References (36)

  • X. Ji et al.

    Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere

    Opt Commun

    (2006)
  • P. Pan

    Spectrum changes of rectangular array beams through turbulent atmosphere

    Opt Commun

    (2013)
  • J. Li et al.

    Influence of non-Kolmogorov atmospheric turbulence on the spectral changes of rectangular array beams

    Opt Laser Technol

    (2015)
  • H. Roychowdhury et al.

    Invariance of spectrum of light generated by a class of quasi-homogenous sources on propagation through turbulence

    Opt Commun

    (2004)
  • S. Xie et al.

    Overview of tissue optics

    Physics

    (1998)
  • V.V. Tuchin

    Tissue optics: light scattering methods and instruments for medical diagnosis

    Bellingham: SPIE

    (2014)
  • X. Chen et al.

    Optical beam propagation in soft anisotropic biological tissues

    OSA Continuum

    (2018)
  • Z.A. Steelman et al.

    Light-scattering methods for tissue diagnosis

    Optica

    (2019)
  • Cited by (20)

    • The singularity of the partially coherent beam in biological tissue

      2022, Results in Physics
      Citation Excerpt :

      The relationship between the intensity distribution and the displacement parameter of hyperbolic sinusoidal Gaussian beam in mouse liver tissue and human upper dermis has been studied [13]. The changes in the coherence properties, the relative intensity and the spectral shift of GSM vortex beams in biological tissues have been investigated [14–16]. However, few types of research on the beam singularity of laser propagating in biological tissues have been reported.

    • Robust transmission of Ince-Gaussian vector beams through scattering medium

      2022, Optik
      Citation Excerpt :

      More and more evidences prove that the vector light field has stronger robustness and scattering resistance through perturbing medium. Different kinds of vectorial structure beams have been expected to mitigate the adverse effects in complex media and used to explore advance imaging, remote sensing and free space optical communication [7–14]. By using Monte Carlo model, Doronin studied the propagation of cylindrical vector beams through the turbid tissue-like scattering medium and these beams have been demonstrated to have higher degree of fringe contrast in comparison to linearly polarized Gaussian beam [15].

    • Propagation of partially coherent hyperbolic sinusoidal Gaussian beam in biological tissue

      2021, Optik
      Citation Excerpt :

      Accordingly, it is investigated that laser array beam having large source size diverges less comparing with beam having small source size [1]. Spectral jump of Gaussian-Schell model vortex beam can be increased if a tissue with stronger turbulence is used [2]. In another study, experimental set-up is established using tissue mimicking phantoms and it is resulted as beams having larger OAM value spread more during propagation [3].

    View all citing articles on Scopus
    View full text