Absolute flatness measurements of silicon mirrors by a three-intersection method by near-infrared interferometry
© Uchikoshi et al.; licensee Springer. 2013
Received: 30 December 2012
Accepted: 18 April 2013
Published: 7 June 2013
Absolute flatness of three silicon plane mirrors have been measured by a three-intersection method based on the three-flat method using a near-infrared interferometer. The interferometer was constructed using a near-infrared laser diode with a 1,310-nm wavelength light where the silicon plane mirror is transparent. The height differences at the coordinate values between the absolute line profiles by the three-intersection method have been evaluated. The height differences of the three flats were 4.5 nm or less. The three-intersection method using the near-infrared interferometer was useful for measuring the absolute flatness of the silicon plane mirrors.
KeywordsAbsolute flatness Silicon Mirror Interferometer Near infrared Phase shift Three-flat method Three-intersection method
High-precision measurements of surface flatnesses are important in the development of optical devices. In flatness testing, interferometry with a standard flat is used for high-precision measurements. In a measurement with a standard flat, the measurement accuracy is mainly determined using the figure of the standard flat. The three-flat method by interferometry is commonly used to measure the flatness of standard flat surfaces for high-precision interferometers. This method allows others to measure the absolute line profile, and its importance is widely accepted [1–4]. The absolute testing of optical flats has been discussed by a rotation-shift method .
High-grade flats are required for interferometry with a standard flat because the accuracy is critically dependent on the figure. Recently, flattened silicon surfaces on the nanometer scale have been prepared [6–8]. A silicon flat is expected to be one of the standard flats. The absolute line profile of the silicon mirror cannot be measured by the three-flat method when a visible light is used. To measure the absolute line profile of the silicon mirror by the three-flat method, an interferometer with a light source where the silicon mirror is transparent must be constructed, and only three silicon mirrors are used to measure the absolute line profiles. However, the absolute line profile measurement of the silicon mirror with a near-infrared light has not been carried out using only silicon mirrors. A near-infrared Fizeau interferometer with a 1.55-μm wavelength laser diode has been developed to improve the fringe contrast for large surface roughness. However, a near-infrared interferometer using a shorter wavelength has not been tested .
The authors constructed an interferometer using a near-infrared laser diode with a 1,310-nm wavelength light where the silicon plane mirror is transparent. They also measured the absolute line profiles of three silicon plane mirrors for standard flats through the use of the three-flat method by near-infrared interferometry . In this paper, the authors describe a method for measuring the absolute flatness of silicon mirrors by a three-intersection method and determine the absolute shapes using a near-infrared interferometer. To evaluate the precision of the absolute flatness measurements, the authors examine the height differences in the absolute shapes.
The relative heights of the reference and detected surface were calculated from the initial phases and the wavelength. Three silicon plane mirrors (A, B, and C flats) were combined in pairs with different positional combinations (transmission reference A and detected B, A and C, and B and C) in the interferometer and used for calculation of the absolute line profile of each silicon plane mirror by the three-flat method . The absolute line profile could be measured only along a vertical center line on the reference and detected flats. The B flat in the combination B and C was rotated around the vertical center line compared to the B flat in the combination A and B. The position of the center and the direction of the center line on the detected flat were adjusted to be the same as those on the reference flat within 1 pixel of the CCD camera (which has 640 × 480 pixels). One pixel corresponds to 107 μm on the flat.
Results and discussion
Height differences at coordinate values
x-y coordinate value
Height difference (nm)
The authors measured the absolute flatness of three silicon plane mirrors with the three-intersection method using the near-infrared interferometer. The height differences at the x-y coordinate values have been examined to evaluate the precision of the absolute flatness measurement. The height differences of the three flats were 4.5 nm or less. The absolute flatness of the surfaces may be measured through the use of the three-intersection method by near-infrared interferometry. This study represents an initial step toward the measurement of flattened silicon surfaces using a near-infrared interferometer.
The work was supported in part by a Grant-in-Aid for Scientific Research (C) 23560123 from Japan Society for the Promotion of Science.
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