Ming-Feng Lu

Method for suppressing the quantization error of Newton’s rings fringe pattern

Abstract. Newton’s rings fringe pattern is often encountered in optical measurement. The digital processing of the fringe pattern is widely used to enable automatic analysis and improve the accuracy and flexibility. Before digital processing, sampling and quantization are necessary, which introduce quantization errors in the fringe pattern. Quantization errors are always analyzed and suppressed in the Fourier transform (FT) domain. But Newton’s rings fringe pattern is demonstrated to be a two-dimensional chirp signal, and the traditional methods based on the FT domain are not efficient when suppressing quantization errors in such signals with large bandwidth as chirp signals. This paper proposes a method for suppressing quantization errors in the fractional Fourier transform (FRFT) domain, for chirp signals occupies little bandwidth in the FRFT domain. This method has better effect on reduction of quantization errors in the fringe pattern than traditional methods. As an example, a standard Newton’s rings fringe pattern is analyzed in the FRFT domain and then 8.5 dB of improvement in signal-to-quantization-noise ratio and about 1.4 bits of increase in accuracy are obtained compared to the case of the FT domain. Consequently, the image quality of Newton’s rings fringe pattern is improved, which is beneficial to optical metrology.

Application of Fractional Fourier transform for interferometry

The Fractional Fourier transform can be understood as a chirp-based decomposition. Accordingly it can be used to process fringe patterns with quadratic phase, including denoising, quantization error reduction, sampling and reconstruction, and phase derivative estimation.

Method for reducing Newton's rings pattern in the scanned image reproduced with film scanners

Newton’s rings pattern always blurs the scanned image when scanning a film using a film scanner. Such phenomenon is a kind of equal thickness interference, which is caused by the air layer between the film and the glass of the scanner. A lot of methods were proposed to prevent the interference, such as film holder, anti-Newton’s rings glass and emulsion direct imaging technology, etc. Those methods are expensive and lack of flexibility. In this paper, Newton’s rings pattern is proved to be a 2-D chirp signal. Then, the fractional Fourier transform, which can be understood as the chirp-based decomposition, is introduced to process Newton’s rings pattern. A digital filtering method in the fractional Fourier domain is proposed to reduce the Newton’s rings pattern. The effectiveness of the proposed method is verified by simulation. Compared with the traditional optical method, the proposed method is more flexible and low cost.

Analysis of Actual Sampled Data System in Fractional Fourier Transform Domain

Sampling and reconstruction is a basic issue in signal processing. The known sampling theory in the fractional Fourier transform (FRFT) domain is based on the assumption of ideal uniform impulse train sampling. However, this assumption is not valid for engineering application. This paper analyzes the actual sample-and-hold system in the FRFT domain, and then constructs a new sample-and-hold system in the FRFT domain to recovery the original input signal. The result obtained in this paper realizes the application of the sampling theorem for the FRFT domain in engineering.

Chirp images in 2-D fractional Fourier transform domain

Chirp signals are very common in radar, communication, sonar, and etc. Little is known about chirp images, i.e., 2-D chirp signals. In fact, such images frequently appear in optics and medical science. Newtons rings fringe pattern is a classical example of the images, which is widely used in optical metrology. It is known that the fractional Fourier transform(FRFT) is a convenient method for processing chirp signals. Furthermore, it can be extended to 2-D fractional Fourier transform for processing 2-D chirp signals. It is interesting to observe the chirp images in the 2-D fractional Fourier transform domain and extract some physical parameters hidden in the images. Besides that, in the FRFT domain, it is easy to separate the 2-D chirp signal from other signals to obtain the desired image.