Precision grating for measuring microscope lens distortions

Abstract

Abstract. Microscopy is used in most technology processes where two-dimensional distributions, that are digital images of the shape and appearance of integrated circuit (IC) features, reveal important information. Optical microscopy and diffraction gratings can be used to measure the placement of IC features with a precision of less than 1 nm (1σ) with a new technique of separately viewing multiple levels. However, the microscope's optical and video camera distortion may cause significant errors in the IC feature measurement under some circumstances. In this paper, the optical and video camera distortions of an optical microscope used in IC feature measurement were studied by analyzing digital images of a precision grating. MATLAB programs were used to extract the value of intensity of each pixel in the grating image. By matching a position dependent, phase-varied ideal sinusoidal wave to the processed grating digital image, the phase of the best-fit sine wave was observed to vary by the equivalent of many nanometers at different locations within the digital image of the grating. This variation was similar, but significantly different, for different microscope objectives. It is believed to arise from optical distortion within the microscope, and possibly also from distortion within the camera. Impact of optic chromatic aberration and microscope stability on the measurement of IC features was also studied. The method described here is inexpensive and easy to implement since it does not require any sophisticated equipment or controlled environment. This technique provides an attractive option for small companies, university labs and instrument manufacturers.

An Approach to Minimising Estimated Pincushion Camera Distortions

“…k is a vector parameter of distortion, and r l is the distance between u and u l . The order of the distortion function is often determined by the length of k. Most authors agreed that for barrel-radial distortions, second or forth order d is sufficient [1], [6], [8]. The proposal for pincushion distortions therefore is:…”

“…The maximum likelihood estimate was obtained by minimizing a nonlinear minimization problem, which was solved with the LevenbergMarquardt Algorithm. The algorithm is well described and implemented by [1], [6], [12], [14].…”

“…However in both cases, the surface area Modern digital cameras with zoom lenses are often the victims of this type of lens aberrations. In some researches including [1], [6], [7], pincushion distortion has been estimated as the amount a reference line is bent to the percentage of the image height. Most consumer digital cameras retain a pincushion distortion much lower than that of the barrel distortion with 0.62% being a typical value [5].…”

“…They do not affect the image quality [1], [5], but, they could become significant for automated applications where time is a factor [5], [6], [7]. Like any other types of distortions, researchers often attribute them to inherent error of the lens [1], [4].…”