Figure shows a schematic diagram of the near-infrared interferometer. The near-infrared interferometer was built based on the Fizeau interferometer. Figure shows a photograph of the near-infrared interferometer. The near-infrared laser diode (FOL13DDRC-A31, Furukawa Electric Co., Ltd., Chiyoda-ku, Tokyo, Japan) with a 1,310-nm peak wavelength light where the silicon plane mirror is transparent, was used as a light source. The typical peak wavelength of the laser light was 1,310 nm. The temperature dependence of the peak emission wavelength was 0.09 nm/°C. The ambient temperature fluctuation during the measurements by the three-flat method was within 0.1°C. The temperature of the laser diode was within 0.1°C. The wavelength fluctuation was estimated to be 0.009 nm from the temperature dependence and fluctuation. The output light from the near-infrared light source was expanded to the necessary size. A parallel light was provided using the collimator and perpendicularly incident on the reference and detected surfaces. The reference and detected surfaces were placed almost parallel, and the distance between them was approximately 24 mm. The light was divided into two waves on the reference surface. One of the waves was reflected on the surface and the other passed through it. The wave passing through the reference surface was reflected on the detected surface. The two reflected waves passing through the imaging lens interfered and formed interferograms. The image of the interferogram was put into a personal computer with a near-infrared charge-coupled device (CCD) camera (C5840, Hamamatsu Photonics K. K., Hamamatsu, Shizuoka, Japan). The CCD camera had a high sensitivity to wavelengths from 400 to 1,650 nm. The signal of the CCD camera output was converted to a 10-bit digital signal using a video analog-to-digital converter. The 32 digital signals were accumulated on a computer with a software (LabVIEW, National Instruments Corporation, Austin, TX, USA) designed to obtain the average. The first 10 digits of the average signal were chosen as the measured value of the interferogram intensity.
Schematic diagram of the near-infrared interferometer.
Photograph of the near-infrared interferometer.
Figure shows a typical intensity map of an interferogram. The distance between the reference and detected surfaces varied by an interval of λ
/12 to λ
/2 with a phase shift stage, and interferograms were recorded at equal intervals of the shifted distance using the CCD camera. The phase shift stage which was composed of elastic hinges and a piezoelectric actuator traveled in a straight line. In order to reduce the effects of environmental vibration or temperature drift on the measurement precision, the reference surface was moved stepwise for the phase shift, and the intensities of the interferograms were averaged on a platform at each step. The reference surface was moved by accelerating or decelerating the drive with the phase shift stage under low acceleration just after starting or before stopping to avoid the drift of the reference surface caused by vibration. Environmental vibration was attenuated using an active vibration-isolated table (AVI-350M, Herz Co., Ltd., Yokohama, Kanagawa, Japan). The acceleration of the environmental vibration was approximately 2 mgal. Both the reference and detected surfaces were silicon plane mirror surfaces. The silicon plane mirror was a square plate with polished surfaces on both sides. To prevent interference by the reflected light from the back surface of the reference or the detected surface, a wedge was formed on the back surface of the silicon plane mirrors. The designed width, thickness, wedge angle, and azimuth angle of the wedge were 50.0 mm, 10.0 mm, 0.28°, and 22.5°, respectively. The silicon plane mirrors were polished with a magnetorheological finishing (MRF) [11
], and the flatnesses were 30 nm or less. The silicon plane mirror was supported at six points on the sample holder which was fixed on the phase shift stage, and the mirror was supported at three points on the back surface, two points on the undersurface, and one point on the side surface.
A typical intensity map of an interferogram.
From the interferogram intensities at each pixel site of the CCD camera, the initial phase of each pixel site was calculated by 6 + 1-sample algorithm [12
]. Figure shows the sampling for the 6 + 1-sample algorithm by the following equation:
Sampling for the 6 + 1-sample algorithm.
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 [2
]. 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.
Figure shows the arrangement of the reference and detected flats in absolute flatness measurements by the three-intersection method. Both rotating and shifting were used to eliminate an indeterminate term that equated to a twisted surface [13
]. In the three-intersection method, the reference flat (the B flat) was rotated around the z
-axis, or the detected flat (the C flat) was shifted from the combination B and C flats in the three-flat method. By rotating the reference flat 90 or -90° clockwise around the z
-axis, as shown in Figure a,b, the absolute line profile could be measured only along a diagonal or another diagonal line on the reference and detected flats. By shifting the detected flat to y
-20.00 mm or x
-20.00 mm using the XZ stage (FS-1100PXZ, SIGMA TECH. CO., LTD., Hanno, Saitama, Japan), as shown in Figure c,d, the absolute line profile could be measured only along a line at y
10.0 mm or x
10.0 mm. Figure shows the test configurations in absolute flatness measurements by the three-intersection method. An absolute line profile could be measured only along a rotation axis on the reference or the detected flat by the three-flat method. Figure a,b,c shows the configuration of the rotation axis on a diagonal, another diagonal and a line at y
10.0 mm, respectively. Heights of the three absolute profiles along the three axes were adjusted to be zero at three intersections indicated by solid circles in Figure c. Five absolute line profiles along the rotation axes parallel to the y
-axis were measured at x
-10.0, -5.0, 0.0, 5.0, and 10.0 mm in Figure d. The height of each profile was adjusted to be the same as that of the profiles at the two intersections indicated by solid circles for y
10.0 mm, one diagonal or for y
10.0 mm, and another diagonal. Thus, an absolute flatness could be measured by the three-intersection method.