Contrast-to-gradient Research Articles

Evaluation of both image resolution and contrast-to-noise ratio in scanning electron microscopy

The contrast-to-gradient (CG) resolution has been defined as a weighted harmonic mean of the local resolution, i.e. the length defining the object's local fine structure at each pixel position. The newly defined resolution Res is defined as 2 sigma/ sqrt 2, where 2 sigma is a sharpness factor of the image pattern obtained by the conversion 2 sigma = ARCG + B using default constants A and B. In the present study, we have extended the algorithm to change the constants from default values to calibrated ones using standard images that are same in both pattern and contrast-to-noise ratio (CNR) as the original SEM image to be evaluated. The calibrated image resolution with a weak noise dependency is evaluated with the CNR as a given parameter.

Influence of a combination of random noise and pattern-edge width (in pixels) on contrast-to-gradient image resolution in scanning electron microscopy

The contrast-to-gradient (CG) method has been proposed previously for the evaluation of image resolution in scanning electron microscopy (SEM). In the CG algorithm, the image to be evaluated is gradually reduced to form the 1/r-reduced image (r = 1, 2, 3, ...) until the representative features of local patterns are accurately recognizable after the corresponding r-th noise reduction. We have studied the influence of a combination of random noise and pattern-edge width (in pixels) on the CG resolution R using both PC-made test images and typical SEM images. As the random noise is larger, the value of R becomes larger (or poorer). The increase in R due to the noise influence is more significant for the narrower width of the pattern edge. This satisfactorily agrees with the common idea that the image resolution is to reflect the sharpness of the pattern edge recognized in the image noise. By revising the form of DeltaR from the weighted standard fluctuation of R to the differential of R, a significantly weak N(dot)-dependency on R has been favorably confirmed, with keeping firmly the noise-dependency on R. Here, N(dot) is the number of pattern dots in the image.

Influence of random noise on the contrast-to-gradient image resolution in scanning electron microscopy

The contrast-to-gradient (CG) method has been proposed previously for the evaluation of image resolution in scanning electron microscopy (SEM). The CG resolution is based on the local resolution, which is defined as the distance to recognize the object's local surface at each pixel position. Then, the CG resolution R is inherently influenced by random noise contained in the image. The present study demonstrates the influence of random noise on the R-values using both personal computer-made dot patterns in various sizes and densities and SEM test micrographs. It is found that the R-values increase with increasing random noise intensity N and their increases are smaller for higher-density patterns, but the R-values are independent of their image sizes under constant pattern density. In addition, the standard CG algorithm is modified especially for straightly fabricated patterns along the x- (or y-) axis, resulting in an improvement in the measurement accuracy of y- (or x-) directional resolutions. The straightness as known information is utilized fully to recognize the local pattern in the random noise.

Contrast-to-gradient method for the evaluation of image resolution taking account of random noise in scanning electron microscopy.

We have taken random image noise into consideration in the contrast-to-gradient (CG) method for the evaluation of image resolution R in scanning electron microscopy (SEM). When looking at the local fine pattern in the SEM micrograph containing much random noise, viewers gradually expand the region of interest (ROI) to improve the signal-to-noise ratio (SNR) and to recognize the pattern. We employed this approach in the CG algorithm to evaluate potential resolution Rpot, which is defined as the minimal/most accurate CG resolution calculated in the ROI expanding process. The image noise or SNR also is evaluated by the parameter deltaR / R, where deltaR is a standard deviation of R. The Rpot values depending on SNR are useful for comparison among images containing different random noise.

Contrast-to-gradient method for the evaluation of image resolution in scanning electron microscopy

In a previous study, we proposed the contrast-to-gradient (CG) method to evaluate the image resolution in scanning electron microscopy. The directional CG resolution R( θ) is defined as a weighted harmonic mean of the local resolution R P ( x, y; θ) having a specified azimuth angle θ, where R P ( x, y; θ) is proportional to the quotient of the threshold contrast divided by the local gradient. The local gradient is calculated from the quadratic function that best fits the local pixel intensities over the region of interest (ROI) of 3×3 or 5×5 pixels in size. The image resolution R(CG) is defined as a geometric mean of the directional resolution R( θ). In this paper we review the characteristics of R(CG)-values, which are intrinsically independent of a black-and-white contrast reversal and of a brightness/contrast change (as long as there is no accompanying saturation/cut-off in the intensity). We also demonstrate the wide range applicability of the CG method for various types of images (such as low-contrast, noise containing, strongly directional, and periodic/non-periodic pattern images as well as ordinary images opposite to the above). As to the encountered problem that the R(CG)-value is slightly overestimated for a rather low-magnification image, we propose a zero-corrected CG method as a prospective solution.

Evaluation of depth of field in SEM images in terms of the information-passing capacity (IPC) and contrast gradient in SEM image

The depth of field (DoF) in scanning electron microscope (SEM) images has been determined by estimating the change of image sharpness or resolution near the exact focus position. The image sharpness or resolution along the optical axis is determined by calculating the information-passing capacity (IPC) of an optical system taking into account the effect of pixel size of the image. The change of image sharpness near the exact focus position is determined by measuring the slope gradient of the line profile in SEM images obtained at various focal positions of beam. The change of image sharpness along the optical axis determined by the IPC agrees well with those determined by the slope gradient of line profiles in SEM images when a Gaussian distribution having radius 0.86 L p ( L p: pixel size in image) at which the intensity has fallen to 1/e of the maximum is applied to the IPC calculation for each pixel intensity. The change of image sharpness near the exact focus position has also been compared with those determined by the CG (Contrast-to-Gradient) method. The CG method slightly underestimates the change of image sharpness compared with those determined by the IPC method.

Contrast-to-gradient method for the evaluation of image resolution in scanning electron microscopy.

In a previous study, we proposed the contrast-to-gradient (CG) method for evaluating image resolution. Here, the CG resolution is defined as a weighted harmonic mean of the local resolution, which is proportional to the quotient of the threshold contrast divided by the local gradient. The local gradient is calculated from the quadratic function that best fits the local pixel intensities over the region of interest (ROI) of 3 x 3 or 5 x 5 pixels in size. To refine the CG method, some modifications are carried out in the present study. Directional resolutions are employed to evaluate images, including astigmatism or strongly directional patterns as well as isotropic patterns. Here, CG resolution is redefined so as to keep the same value even for the image reversed in black-and-white contrast, because of no difference in the image information during contrast reversing. Besides, CG resolution is characterized to be independent of the brightness/contrast change unless these changes do not bring about both cut-off and saturation in the pixel intensities. Dependencies of the denoising effect and the resolution accuracy on ROI size are demonstrated as a function of image-noise.

A method for personal expertise-independent evaluation of image resolution in scanning electron microscopy.

The two conventional methods currently employed for the evaluation of image resolution in scanning electron microscopy are the gap method and a fast Fourier transform (FFT) method. These can be highly dependent on personal expertise on the distinction between signal information and noise contained in a micrograph. Hence, the present paper proposes an alternative method (referred to as a contrast-to-gradient (CG) method) that can determine the image resolution of a micrograph without requiring personal expertise on the judgment of noise. The image resolution in the CG method is defined as a weighted harmonic mean of the local resolution, which is proportional to the quotient of the threshold contrast divided by the local gradient. The local gradient is calculated from the quadratic function that best fits the local pixel intensities over 5 x 5 pixels. It has been shown that the CG method, compared with the FFT method, has a broader range of applications for various types of images, such as low-contrast, noise-containing, filter-processed, highly directional, and quasi-periodic feature images.