Scalar-based speckle simulation model from the angular surface scattering based on generalized Harvey-Shack theory for laser displays

Highlights

• A speckle simulation model based on angular surface scattering is proposed.

• The proposed model simulates speckles with angular surface scattering theory.

• The proposed simulation model can generate similar speckles from a laser display.

• A speckle is studied as a function of detection angle by simulation and experiment.

Abstract

A speckle simulation model based on the angular surface scattering from the analyzed rough surface is proposed for laser applications. For computationally efficient simulation model for the far-field and large-area screen, the generalized Harvey−Shack theory was used to calculate the angular scattering of rough surface that was geometrically analyzed considering the roughness and the lateral correlation length. A laser display was selected as a reference system to validate the simulation result and it was found that the proposed simulation model can generate almost similar speckle patterns with a speckle contrast ratio of 0.7095 compared to that of 0.7066 from experimental measurement.

Introduction

Laser-based displays have recently received much attention due to their advantages such as high illuminance, small beam size, low power consumption, and small device size [1], [2], [3], [4], [5]. While these devices can be used in a variety of applications, they suffer from a critical drawback related to speckles, which represent a granular intensity pattern produced by a diffuse reflection of coherent light from a non-smooth surface [5], [6], [7]. The amount of speckle pattern is usually defined in terms of the speckle contrast ratio (CR) which has a value from 0 to 1 as follows,

$$\mathit{CR}=\frac{\sigma }{〈I〉}=\frac{\sqrt{〈I^2〉-〈I{〉}^2}}{〈I〉}$$

where $〈$I$〉$ and σ are the mean and the standard deviation of the intensity of a given image, respectively. Speckles degrade the quality of images produced by optical components that use coherent light sources [8], [9], [10], [11], [12], [13], so the speckles must be reduced to enhance the image quality for laser display applications. For the reduced speckles, spatial and temporal coherence of a laser beam are carefully controlled by manipulating its wavelength, polarization, and angle [13].

A numerical simulation can be a good approach for better understanding about the generation of speckles from rough surfaces in a laser display. Some numerical simulations were proposed with scalar and vector calculations based on random speckle generation. In scalar-based simulations, speckles are produced theoretically using the scalar diffraction theory such as Fresnel or Fraunhofer diffraction with some assumptions, which enables computationally simple and efficient for the light propagation [14], [15]. A simple scalar method was proposed by diffraction theory including random factor that represents the roughness of media expressed in phase information [14]. Another scalar speckle simulation was also reported that the proposed algorithm generates the speckles effectively using the probability density function and speckle correlation coefficient for various cases [15]. On the other hand, vector-based simulation was also used to generate speckles utilizing the electric and magnetic fields based on Maxwell’s equations, which is highly accurate but computationally complex [16].

In the case of speckle simulation for a laser display, the specific surface profile and angular scattering characteristic is important to calculate the accurate speckle patterns. Because speckle occurs due to the interference between the rough surface and coherent light, speckle patterns strongly depend on the surface profile as well as detection angle from the surface. For accurate prediction of speckle patterns, thus exact surface profile must be analyzed considering specific distribution of height and lateral correlation length from the surface roughness. Also, the detection angle dependence on speckles has been analyzed and discussed [17], [18]. Since a laser display is subject to the far-field and large area illumination, it is important to understand exact speckle patterns as a function of viewing angle. Thus, a new speckle simulation model is required to obtain the view angle dependence using angular surface scattering analysis from rough surfaces with exact specific profile data to be applied for a laser display.

In this paper, we propose a scalar-based simulation model for speckles using the angular scattering theory from rough surfaces. The generalized Harvey-Shack (GHS) theory was applied to evaluate the angular scattering characteristics of the reflected beam from the rough surface, where its geometric characteristic was analyzed from the root-mean-square (RMS) data with a concept of lateral correlation length. From the angular scattering data, speckle patterns were generated as a function of detection angle, which located long distance from the surface. To validate the proposed speckle simulation model, the simulated speckles were compared to those of the experimentally measured speckles for a laser display. Since the proposed model can realize the speckle patterns as a function of viewing angle using the scalar-based approach, it can be easily adopted for the large-area and far-field applications of laser display with a cost-effective computation.