Katsuichi Kitagawa

Single-shot surface profiling by local model fitting

A new surface profiling algorithm called the local model fitting (LMF) method is proposed. LMF is a single-shot method that employs only a single image, so it is fast and robust against vibration. LMF does not require a conventional assumption of smoothness of the target surface in a band-limit sense, but we instead assume that the target surface is locally constant. This enables us to recover sharp edges on the surface. LMF employs only local image data, so objects covered with heterogeneous materials can also be measured. The LMF algorithm is simple to implement and is efficient in computation. Experimental results showed that the proposed LMF method works very well.

Thin-film thickness profile measurement by three-wavelength interference color analysis

Conventional transparent film thickness measurement methods such as spectroscopy are essentially capable of measuring only a single point at a time, and their spatial resolution is limited. We propose a film thickness measurement method that is an extension of the global model-fitting algorithm developed for three-wavelength interferometric surface profiling. It estimates the film thickness distribution from an interference color image captured by a color camera with three-wavelength illumination. The proposed method is validated through computer simulations and experiments.

Fast surface profiler by white-light interferometry using a new algorithm, the SEST algorithm

We devise a fast algorithm for surface profiling by white- light interferometry. It is named the SEST algorithm after Square Envelope function estimation by Sampling Theory. Conventional methods for surface profiling by white-light interferometry based their foundation on digital signal processing technique, which is used as an approximation of continuous signal processing. Hence, these methods require narrow sampling intervals to achieve good approximation accuracy. In this paper, we introduce a totally novel approach using sampling theory. That is, we provide a generalized sampling theorem that reconstructs a square envelope function of a white-light interference fringe from sampled values of the interference fringe. A sampling interval in the SEST algorithm is 6-14 times wider than those of conventional methods when an optical filter of the center wavelength 600 nm and the bandwidth 60 nm is used. The SEST algorithm has been installed in a commercial system which achieved the worlds fastest scanning speed of 42.75 micrometers /s. The height resolution of the system lies in the order of 10 nm for a measurement range of greater than 100 micrometers .

Two-wavelength single-shot interferometry

A new surface profiling technique is proposed, which enables us to measure a surface profile without a rounding effect and with extended phase measurement range. It is accomplished by a newly developed two-wavelength imaging system and the local model fitting (LMF) algorithm for carrier pattern analysis. The experimental results demonstrated that the proposed method can measure steep steps fast and accurately with an extended measurement range, while the robustness against vibration of the conventional single-shot methods is maintained.

Automatic parameter optimization of the local model fitting method for single-shot surface profiling

The local model fitting (LMF) method is a single-shot surface profiling algorithm. Its measurement principle is based on the assumption that the target surface to be profiled is locally flat, which enables us to utilize the information brought by nearby pixels in the single interference image for robust LMF. Given that the shape and size of the local area is appropriately determined, the LMF method was demonstrated to provide very accurate measurement results. However, the appropriate choice of the local area often requires prior knowledge on the target surface profile or manual parameter tuning. To cope with this problem, we propose a method for automatically determining the shape and size of local regions only from the single interference image. The effectiveness of the proposed method is demonstrated through experiments.

Iteratively-reweighted local model fitting method for adaptive and accurate single-shot surface profiling

The local model fitting (LMF) method is one of the useful single-shot surface profiling algorithms. The measurement principle of the LMF method relies on the assumption that the target surface is locally flat. Based on this assumption, the height of the surface at each pixel is estimated from pixel values in its vicinity. Therefore, we can estimate flat areas of the target surface precisely, whereas the measurement accuracy could be degraded in areas where the assumption is violated, because of a curved surface or sharp steps. In this paper, we propose to overcome this problem by weighting the contribution of the pixels according to the degree of satisfaction of the locally flat assumption. However, since we have no information on the surface profile beforehand, we iteratively estimate it and use this estimation result to determine the weights. This algorithm is named the iteratively-reweighted LMF (IRLMF) method. Experimental results show that the proposed algorithm works excellently.

Interpolated local model fitting method for accurate and fast single-shot surface profiling

The local model fitting (LMF) method is a useful single-shot surface profiling algorithm based on spatial carrier frequency fringe patterns. The measurement principle of the LMF method relies on the assumption that the target surface is locally flat. In this paper, we first analyze the measurement error of the LMF method caused by violation of the locally flat assumption. More specifically, we theoretically prove that the measurement error is zero at fringe intensity extrema in an interference pattern even when the locally flat assumption is violated. Based on this theoretical finding, we propose a new surface profiling method called the interpolated LMF (iLMF) algorithm, which is more accurate and computationally efficient than the original LMF method. The practical usefulness of the iLMF method is shown through experiments.

Multiwavelength-integrated local model fitting method for interferometric surface profiling

The local model fitting (LMF) method is a useful single-shot surface profiling algorithm that features fast measurement speed and robustness against vibration. However, the measurement range of the LMF method (i.e., measurable height difference between two neighboring pixels) is limited up to a quarter of the light source wavelength. To cope with this problem, the multiwavelength-matched LMF(MM-LMF) method was proposed, where the plain LMF method is first applied individually to interference images obtained from multiple light sources with different wavelengths, and then the LMF solutions are matched to obtain a range-extended solution. Although the MM-LMF method was shown to provide high measurement accuracy under moderate noise, phase unwrapping errors can occur if individual LMF solutions are erroneous. In this paper, we propose the multiwavelength-integrated LMF (MI-LMF) method, which directly computes a range-extended solution from multiple interference images in an integrated way. The effectiveness of the proposed MI-LMF method is demonstrated through simulations and actual experiments.

Fabrication of optical multilayer for two-color phase plate in super-resolution microscope

In super-resolution microscopy based on fluorescence depletion, the two-color phase plate (TPP) is an indispensable optical element, which can independently control the phase shifts for two beams of different color, i.e., the pump and erase beams. By controlling a phase shift of the erase beam through the TPP, the erase beam can be modulated into a doughnut shape, while the pump beam maintains the initial Gaussian shape. To obtain a reliable optical multiplayer (ML) for the TPP, we designed a ML with only two optical layers by performing numerical optimization. The measured phase shifts generated by the fabricated ML using interferometry correspond to the design values. The beam profiles in the focal plane are also consistent with theoretical results. Although the fabricated ML consists of only two optical layers, the ML can provide a suitable phase modulation function for the TPP in a practical super-resolution microscope.

Improved algorithm for multiwavelength single-shot interferometric surface profiling: speeding up the multiwavelength-integrated local model fitting method by local information sharing.

The local model fitting (LMF) method is a single-shot interferometric surface profiling algorithm that possesses nondestructive, fast, accurate, and robust measurement capabilities. To extend the measurement range of LMF, extensions based on multiwavelength light sources such as the multiwavelength-matched LMF (MM-LMF) method and the multiwavelength-integrated LMF (MI-LMF) method were proposed recently. MM-LMF is computationally efficient but it tends to suffer from phase unwrapping errors, whereas MI-LMF tends to be accurate but it is computationally expensive. In this paper, we improve the computational efficiency of MI-LMF by combining it with MM-LMF via local information sharing. Through actual experiments, we demonstrate that the proposed method is approximately 10 times faster than the original MI-LMF method, with measurement accuracy kept comparable.