2.1.

LDF Unit

The LDF unit is subdivided into laser delivering, signal detection, and sharing paths. The source of the LDF unit in the laser delivering path is a polarized laser diode (LDF-LD, Thorlabs L780P010) at center wavelength of 780 nm. The s-polarized laser beam from the source has a divergence angle of about 30 deg and, hence, two aspheric lenses (LDF-L₁ and LDF-L₂) are implemented to shrink its divergence enabling enough power to the targeted vessels. After reflection by a polarization beam splitter (LDF-beam splitter), the light goes to two lenses (LDF-L₃ and LDF-L₄), and is then redirected to the sharing path by a dichroic beam splitter (SP-beam splitter). An accommodation lens (SP-L₁) followed by two lenses (SP-L₂ and SP-L₃) in the sharing path is adopted for patients with myopia or hypermetropia. The delivered laser spot at the position of the cornea is about 2 mm in diameter with an output power of less than 150 μW, which is safe for continuous examination of 20 min according to ANSI Z136.1. Backscattered light from the target retraces the light path of the delivering light until the signal detection path is separated by the LDF-beam splitter, where the transmitted light with p-polarization owing to birefringence of the cornea and other components is collected by a fiber pigtailed avalanche photon detector (APD). The detected signal is then amplified for further processing.

2.2.

Illumination Unit

The illumination unit is constructed by replacing the halogen bulb in a KOWA camera with a green-light LED (IU-LED) at 530 nm. The maximum output power is 10 mW and can be modified by adjusting the current feeding to the IU-LED.

2.3.

Observation Unit

Besides optical components in the sharing path mentioned above, the observation unit is constructed by two additional lenses (OU-Ocular and OU-L₁) and a targeting plate in between. The targeting plate is located in conjugate to the LDF laser spot on the eye fundus. Under the illumination of IU-LED and with the help of the targeting plate, the observation unit is used to help the operator to adjust the portable LDF for correct positioning of the LDF laser spot on targeted vessels.

The picture of the developed LDF under operation is shown in Fig. 1b. The developed LDF is weighted about 2 kg with compact size, suitable to be carried and operated by hand. Such portable LDF is therefore applicable to special patients such as new born babies, disabled persons, and patients under intensive care or even under operation.

3.1.

Ray Trace Model

In order to explain the mechanism of detection and sensitivity enhancement of the LDF based on the scattering plate, a ray trace model is built to describe the process that the laser transmits from the LDF to the eye fundus and that is scattered by moving red blood cells (RBCs) back to the LDF. As shown in Fig. 2, the model consists of a single blood vessel containing moving RBCs, a convex eye lens with focal length f _c and clear aperture radius r _c, and a scattering plate between the LDF unit and the eye lens with a distance L away from the latter. Due to the scattering characteristics of the scatting plate, the LDF laser illuminates an area over the choroidal bed where static structures and RBCs moving in random directions and velocities are available. Without loss of generality, only one blood vessel perpendicular to the optics axis of the LDF (dotted-dashed line) with RBCs moving at typical azimuth angle (bold arrow) is assumed. Such an assumption of a blood vessel is just for explanation of the mechanism of sensitivity enhancement and is not a realistic mimic of the vascular vessels in the choroidal vascular bed.

Fig. 2

Ray trace model of LDF measurement on the human eye.

A Cartesian coordinate system with origin at the focus of the eye lens is set, where y-axis coincides with the given blood vessel and z-axis along the optics axis of the LDF unit. As shown in Fig. 2, I _i represents an incident ray from the LDF unit illuminating the scattering plate at point (x _i, y _i, L + f _c), and [TeX:] $I_i^\prime $ $I_i^{\prime }$ is one of the scattering components with a separation angle β corresponding to I _i after transmitting through the scattering plate. When ray [TeX:] $I_i^\prime $ $I_i^{\prime }$ passes through the eye lens, it is denoted by ray [TeX:] $I_i^{\prime\prime}$ $I_i^{\prime \prime }$ and hits the given blood vessel at point (0, y ₀, 0). Backscattering happens at point (0, y ₀, 0) and the backscattering intensity is expressed by [TeX:] $I_s = \eta I_i^{\prime\prime}$ $I_s=\eta I_i^{\prime \prime }$ . Here, uniform back scattering coefficient of ηis assumed because of relatively small numerical aperture of human eye and hence limited scattering angle resulting in insignificant angular intensity changes according to Mie theory. Ray [TeX:] $I_s^\prime $ $I_s^{\prime }$ comes from ray I _s after refracted by the eye lens is parallel to ray [TeX:] $I_i^\prime $ $I_i^{\prime }$ and hits the scattering plate at point (x _s, y _s, L + f _c). Ray [TeX:] $I_s^{\prime\prime}$ $I_s^{\prime \prime }$ represents one of the scattering components with a deviation angle of θ₁ relative to the direction of the ray donated by [TeX:] $I_s^\prime $ $I_s^{\prime }$ , and a deviation angle of θ₂ relative to the direction of the z-axis. Doppler frequency shift achieved in ray [TeX:] $I_s^{\prime\prime}$ $I_s^{\prime \prime }$ corresponding to ray I _i based on previous ray tracing is then given by^{14 — 16}

Supposing the incident laser beam from LDF has a Gaussian distribution with maximum intensity of I ₀ and radius of beam waist equals to r _c, the intensity of ray I _i is then determined by [TeX:] $I_i = I_0 \exp [ - \frac{{2x_i ^2 + 2y_i ^2 }}{{r_c ^2 }}]$ $I_i=I_0\exp [-\frac{2x_i^2+2y_i^2}{r_c^2}]$ . When light transmits through the scattering plate, the probability distribution (PS _HG) of the scattering light versus the scattering angle β can be modeled using the Henyey–Greenstein function^{17, 18}

3.2.

Simulation Based on the Model

In order to show how the scattering plate influences the measurement results, numerical simulation of P(f _d) and ChBSpeed is conducted to evaluate both the change of the DSPDS [P(f _d)] curve and the change of ChBSpeed value after the adoption of the scattering plate. The simulation under “normal condition” that the scattering plate is not utilized is achieved as the limit of Eq. 4 when g→1, supposing the redirection capability of the scattering plate can be ignored. The simulation under “scattering condition” after the adoption of the scattering plate uses g = 0.71, which equals the asymmetry factor of the scattering plate in our later experiments. In the simulation under both conditions, f _c is chosen to be 17 mm, which equals the effective focal length of the human eye, and L, r _c, β_max, and θ_2max are set to be 5 mm, 2.5 mm, 25 deg, and 20 deg, respectively.

The curves in Fig. 3a show simulated P(f _d) curve under scattering and normal conditions. The RBC's velocity is set to be 10 mm/s in this simulation. Comparing the curve under scattering condition to that under the normal condition, broadening of P(f _d) and improved power density of higher Doppler frequency shift can be observed. As the P(f _d) curve is broadened and the power density of higher Doppler frequency shift is increased under the scattering condition, the calculated value of ChBSpeed, which corresponds to the first moment of P(f _d) divided by its 0th moment, is calculated to be higher due to utilization of the scattering plate. Fig. 3b shows how the value of ChBSpeed changes versus the alternation of the RBC's velocity. The value of ChBSpeed is linear to the RBC's velocity both under normal and scattering conditions. It can be seen that under the scattering condition, the slope of ChBSpeed versus RBC's velocity is increased, and hence the sensitivity of the speed measurement is enhanced.

Fig. 3

(a) Simulated curves on P(f _d) versus f _d at typical assumed flowing velocity and (b) linear fitting curves on estimated values of ChBSpeed versus RBCs’ velocity under normal and scattering conditions, respectively.

3.3.

Monte Carlo Simulation

In order to show how the scattering plate influences the measured results, we also conduct a Monte Carlo simulation in which, comparing to the ray trace model, the single blood vessel is replaced by a simulated choroidal vascular bed. The main part of the simulation code is adopted from “Monte Carlo modeling of light transport in Multilayered tissues,”²¹ which simulates the photon transports in layers of types of “tissue” and “glass” taking no account of Doppler effect. We modify the code in such a way that it allows us to consider Doppler frequency shift of a scattered photon and direction change of a photon due to a lens. The frequency shift is calculated by the incident and scattered wavenumber vectors of the photon and the velocity vector of the moving particle.¹⁵ The lens is modeled as a lens-layer that refracts the direction of passed photons in terms of Gaussian optics.

In our simulation, the scattering plate is modeled as a layer with the thickness t = 2 mm, the anisotropy factor g = 0.71, the scattering coefficient μ_s = 500 m⁻¹, and the absorption coefficient μ_a→0. The eye lens is modeled as a lens-layer with the focal length f = 17 mm. The vitreous body is modeled as a glass-layer with refractive index n = 1.336 since its μ_s and μ_a are very small. The choroidal vascular bed is modeled as a tissue-layer with t = 0.2 mm, g = 0.87, μ_s = 1.35×10⁵ m⁻¹, and μ_a = 6.13×10⁴ m⁻¹.²² The velocity vector of moving RBCs in this layer is determined by three random numbers: the magnitude with normal distribution (mean: 10 mm/s, standard deviation: 3 mm/s), the azimuth angle with uniform distribution (0 ~ 2π), and the elevation angle with normal distribution (mean: 0, standard deviation: π/2). We choose a concentration of 10% as the times-ratio of Doppler scattering over non-Doppler scattering, considering that in the choroidal vascular bed most part of the tissue is static. Under each condition, 2×10⁶ photons are launched. The schematic of the layers is shown in Fig. 4a with the path of a typical photon marked by the dashed line. The simulation results are plotted in log scale in Fig. 4b and normalized by the maximums, where the solid line is the DSPDS under the normal condition and the dotted line is the DSPDS under the scattering condition, improved power density of higher Doppler frequency shift can also be observed. In order to study how the measured signal is influenced by the multiple scattering within the choroid vascular bed, the scattering times both for Doppler and non-Doppler scattering are recorded. The average scattering times are evaluated to be 1.0 and 1.5 for photons contributed to Doppler and non-Doppler scattering, respectively, shown in Fig. 4c. It means that most of the photons that are collected by the LDF undergo single scattering instead of multiple scattering with the red blood cells. Hence, the single scattering assumption in the ray trace model depicted in Fig. 2 is valid and multiple backscattering in the choroid vascular bed has a negligible effect on the DSPDS. The same conclusion is obtained in Ref. 23 where there is no scattering plate.

Fig. 4

Schematic of (a) the layers in Monte Carlo simulation with the path of a typical photon marked by the dashed line, (b) the simulated DSPDS [P(f _d)] curves under normal and scattering conditions, and (c) the weight of collected photons over scattering times.