Microscope autofocus algorithm based on number of image slope variations.

This paper presents a passive autofocus algorithm applicable to interferometric microscopes. The proposed algorithm uses the number of slope variations in an image mask to locate the focal plane (based on focus-inflection points) and identify the two neighboring planes at which fringes respectively appear and disappear. In experiments involving a Mirau objective lens, the proposed algorithm matched the autofocusing performance of conventional algorithms, and significantly outperformed detection schemes based on zero-order interference fringe in dealing with all kinds of surface blemish, regardless of severity. In experiments, the proposed algorithm also proved highly effective in cases without fringes.

Modified detection scheme for locating phase jumps and reducing detection errors.

Most phase unwrapping algorithms shift the 2π phase jump pixels to obtain the unwrapped phases, while most filtering algorithms remove the noisy pixels to avoid the fault of unwrapped phases. Thus, finding the positions of phase jump pixels and noisy pixels is important. This study proposed a modified detection scheme developed from the originally published noise and phase jump detection scheme [Opt. Express 19, 3086 (2011)]. The original detection scheme finds the noise positions and phase jump positions, and then marks these pixels in two maps, namely, the noise map and the phase jump map. One 2π phase jump contains a 2π-high position and a 0-low position. However, the original detection scheme usually finds a 2π-high position and misses a corresponding 0-low position, or usually finds a 0-low position and misses a corresponding 2π-high position. Moreover, the original detection scheme produces detection errors, containing the repeated pixels of phase jump or the wrong pixels generated by noise. Fortunately, the proposed modified detection scheme can find both the 2π-high position and the corresponding 0-low position. Moreover, the detection errors are also reduced by the proposed modified detection scheme. The robustness of the modified detection scheme is demonstrated both numerically and experimentally.

Integration of robust filters and phase unwrapping algorithms for image reconstruction of objects containing height discontinuities.

For 3D objects with height discontinuities, the image reconstruction performance of interferometric systems is adversely affected by the presence of noise in the wrapped phase map. Various schemes have been proposed for detecting residual noise, speckle noise and noise at the lateral surfaces of the discontinuities. However, in most schemes, some noisy pixels are missed and noise detection errors occur. Accordingly, this paper proposes two robust filters (designated as Filters A and B, respectively) for improving the performance of the phase unwrapping process for objects with height discontinuities. Filter A comprises a noise and phase jump detection scheme and an adaptive median filter, while Filter B replaces the detected noise with the median phase value of an N × N mask centered on the noisy pixel. Filter A enables most of the noise and detection errors in the wrapped phase map to be removed. Filter B then detects and corrects any remaining noise or detection errors during the phase unwrapping process. Three reconstruction paths are proposed, Path I, Path II and Path III. Path I combines the path-dependent MACY algorithm with Filters A and B, while Paths II and III combine the path-independent cellular automata (CA) algorithm with Filters A and B. In Path II, the CA algorithm operates on the whole wrapped phase map, while in Path III, the CA algorithm operates on multiple sub-maps of the wrapped phase map. The simulation and experimental results confirm that the three reconstruction paths provide a robust and precise reconstruction performance given appropriate values of the parameters used in the detection scheme and filters, respectively. However, the CA algorithm used in Paths II and III is relatively inefficient in identifying the most suitable unwrapping paths. Thus, of the three paths, Path I yields the lowest runtime.

Robust detection scheme on noise and phase jump for phase maps of objects with height discontinuities--theory and experiment.

This paper proposes a robust noise and phase jump detection scheme for noisy phase maps containing height discontinuities. The detection scheme has two primary functions, namely to detect the positions of noise and to locate the positions of the phase jumps. Generally speaking, the removal of noise from a wrapped phase map causes a smearing of the phase jumps and therefore leads to a loss of definition in the unwrapped phase map. However, in the proposed scheme, the boundaries of the phase jump regions are preserved during the noise detection process. The validity of the proposed approach is demonstrated using the simulated and experimental wrapped phase maps of a 3D object containing height discontinuities, respectively. It is shown that the noise and phase jump detection scheme enables the precise and efficient detection of three different types of noise, namely speckle noise, residual noise, and noise at the lateral surfaces of the height discontinuities. Therefore, the proposed scheme represents an ideal solution for the pre-processing of noisy wrapped phase maps prior to their treatment using a filtering algorithm and phase unwrapping algorithm.