Analysis of laser speckle severity, granularity, and anisotropy using the power spectral density in polar- coordinate representation

The conventional speckle contrast measures only speckle severity, and is unable to characterize granularity and anisotropy in displayed images, which are easily picked up by human observers. Here, we propose a comprehensive method based on the power spectral density which allows the simultaneous measurement of three components of laser speckle-severity, granularity and anisotropy—as a superior way to evaluate both speckle and speckle reduction techniques. 1 Introduction Speckle arises from coherent interference, such as of laser light that is reflected off a rough surface, and manifests itself as random granular noise. 1,2 Such speckle patterns can be useful, such as in speckle metrology, 3 dynamic speckle inter-ferometry, 4 and speckle profilometry, 5 but in many other applications, speckle is unwanted and results in loss of information , such as in ultrasound imaging. 6 In particular, speckle is detrimental to laser-based imaging systems, such as laser-based televisions (TVs) and projectors, 7–9 and holographic display systems, 10 as it introduces aesthetically displeasing noise. It is thus essential to have a metric which is able to accurately characterize speckle noise and speckle reduction techniques for laser display purposes. The most commonly used metric to evaluate speckle severity is the speckle contrast (C ¼ σ∕hIi), defined as the standard deviation of intensity normalized by the mean intensity. 1,2 This is sufficient in applications where the information in a signal or image is contained only in the individual intensity values and not in correlations between neighboring pixels. In a displayed image, however, local correlations in intensities are essential to define edges, boundaries and features, and the speckle contrast, being a pixel-centric method, is unable to pick up speckle features related to such local correlations. Two examples of such features are granularity and anisotropy in the speckle pattern. In particular, anisotropy can be a pertinent problem—many speckle reduction methods require some form of " movement " in order to break spatial coherence and reduce speckle. These methods can involve both hardware, such as rotating diffusers, 11 or software, such as cyclically shifting the holo-gram. 12 If there was any anisotropy in the application of these methods, the spatial coherence and consequently speckle would be retained along certain directions, resulting in an anisotropic distribution of speckle. An example of how speckle degrades the aesthetic quality of displayed images