Ultraprecise aspheric mirrors that offer nanofocusing and high coherence are indispensable for developing third-generation synchrotron radiation and X-ray free-electron laser sources. In industry, the extreme ultraviolet (wavelength: 13.5 nm) lithography used for high-accuracy aspheric mirrors is a promising technology for fabricating semiconductor devices. In addition, ultraprecise mirrors with a radius of curvature of less than 10 mm are needed in many digital video instruments. We developed a new type of nanoprofiler that traces the normal vector of a mirror's surface. The principle of our measuring method is that the normal vector at each point on the surface is determined by making the incident light beam on the mirror surface and the reflected beam at that point coincide, using two sets of two pairs of goniometers and one linear stage. From the acquired normal vectors and their coordinates, the three-dimensional shape is calculated by a reconstruction algorithm. The characteristics of the measuring method are as follows: the profiler uses the straightness of laser light without using a reference surface. Surfaces of any shape can be measured, and there is no limit on the aperture size. We calibrated this nanoprofiler by considering the system error resulting from the assembly error and encoder scale error, and evaluated the performance at the nanometer scale. We suppressed the effect of random errors by maintaining the temperature in a constant-temperature room within ±0.01°C. We measured a concave spherical mirror with a radius of curvature of 400 mm and a flat mirror and compared the results with those obtained using a Fizeau interferometer. The profiles of the mirrors were consistent within the range of system errors.

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Profile measurement of concave spherical mirror and a flat mirror using a high-speed nanoprofiler.

Processing technology using an extreme ultraviolet light source, e.g., next-generation lithography, requires next-generation high-accuracy mirrors. As it will be difficult to attain the degree of precision required by next-generation high-accuracy mirrors such as aspherical mirrors through conventional processing methods, rapid progress in nanomeasurement technologies will be needed to produce such mirrors. Because the measuring methods used for the surface figure measurement of next-generation mirrors will require high precision, we have developed a novel nanoprofiler that can measure the figures of high-accuracy mirrors without the use of a reference surface. Because the accuracy of the proposed method is not limited by the accuracy of a reference surface, the measurement of free-form mirrors is expected to be realized. By using an algorithm to process normal vectors and their coordinate values at the measurement point obtained by a nanoprofiler, our measurement method can reconstruct three-dimensional shapes. First, we measured the surface of a concave spherical mirror with a 1000-mm radius of curvature using the proposed method, and the measurement repeatability is evaluated as 0.6 nm. Sub-nanometer repeatability is realized, and an increase in the repeatability would be expected by improving the dynamic stiffness of the nanoprofiler. The uncertainty of the measurement using the present apparatus is estimated to be approximately 10 nm by numerical simulation. Further, the uncertainty of a Fizeau interferometer is also approximately 10 nm. The results obtained using the proposed method are compared with those obtained using a Fizeau interferometer. The resulting profiles are consistent within the range of each uncertainty over the middle portions of the mirror.

Three-dimensional surface figure measurement of high-accuracy spherical mirror with nanoprofiler using normal vector tracing method.

High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method

Ultraprecise aspherical mirrors that offer nanofocusing and high coherence are indispensable for developing third-generation
synchrotron radiation and X-ray free electron laser sources. In industry, the extreme ultraviolet
(wavelength: 13.5 nm) lithography used for high-accuracy aspheric mirrors is a promising technology for fabricating
semiconductor devices. In addition, ultraprecise mirrors with a radius of curvature of less than 10 mm are needed in
many digital video instruments. We developed a new type of nanoprofiler that traces the normal vector of a mirror’s
surface. The principle of our measuring method is that the normal vector at each point on the surface is determined
by making the incident light beam on the mirror surface and the reflected beam at that point coincide, using two sets
of two pairs of goniometers and one linear stage. From the acquired normal vectors and their coordinates, the three-dimensional
shape is calculated by a reconstruction algorithm. The characteristics of the measuring method are as
follows. The profiler uses the straightness of laser light without using a reference surface. Surfaces of any shape can
be measured, and there is no limit on the aperture size. We calibrated this nanoprofiler by considering the system
error resulting from the assembly error and encoder scale error, and evaluated the performance at the nanometer
scale. We suppressed the effect of random errors by maintaining the temperature in a constant-temperature room
within ±0.01°C. We measured a concave spherical mirror with a radius of curvature of 400 mm and a flat mirror,
and compared the results with those obtained using a Fizeau interferometer. The profiles of the mirrors were
consistent within the range of system errors.

Development of a nanoprofiler using the follow-up normal vector to the surface for next-generation ultraprecise mirrors

Effects of a laser beam profile to measure an aspheric mirror on a high-speed nanoprofiler using normal vector tracing method

A new high-speed nanoprofiler was developed in this study. This profiler measures normal vectors and their coordinates on the surface of a specimen. Each normal vector is determined by making the incident light path and the reflected light path coincident using five-axis simultaneously controlled stages. From the acquired normal vectors and their coordinates, the three-dimensional shape is calculated by a reconstruction algorithm. In this study, a concave spherical mirror with a 400 mm radius of curvature was measured. As a result, a peak of 30 nm PV was observed at the centre of the mirror. Measurement repeatability was 1 nm. In addition, cross-comparison with a Fizeau interferometer was implemented and the results were consistent within 10 nm. In particular, the high spatial frequency profile was highly consistent, and any differences were considered to be caused by systematic errors.

Development of a High-Speed Nanoprofiler Using Normal Vector Tracing

A new ultra-precision profiler has been developed in order to measure such as asymmetric and aspheric profiles. In the
present study, the normal vectors at each points on the surface are determined by the reflected light beam goes back
exactly on the same path as the incident beam. The surface gradients at each point are calculated from the normal vector
and the surface profile is obtained by integrating the gradient. The measuring instrument was designed according to the
above principle of the measuring method. In the design, four 
ultra-precision goniometers were applied to the adjustment
of the light axis for the normal vector measurement. In the measuring instrument, the angle-positioning resolution and
accuracy of each goniometer are respectively 1.8x10 -8 rad and 2x10 -7 rad. A coaxial with an off-axis parabolic mirror has
been developing for applying as an optical cavity. The most important engineering technique is to measure the profile of
the reflective surface with sub nanometer. The present measuring instrument is evaluating to have capability to the
surface measuring accuracy with nanometer for such parabolic mirror profile measurement. A coaxial off-axis parabolic
mirror with 150 mm focal length has been polished. The outside and inside diameter of the mirror is 360 mm and 258
mm respectively. The thickness of the coaxial direction is 50 mm. The focal point is located on the center of the coaxial
and the center of the coaxial direction of the mirror. The profile measurement such a mirror has been demonstrated.
Specially, self calibration method for increasing the measured position accuracy from measured data is discussed.

Surface gradient integrated profiler for x-ray and EUV optics: self calibration method of measured position for an off-axis parabolic mirror (f=150mm) measurement

The development of a high-speed nanoprofiler is essential for developing the next generation of ultraprecision aspheric mirrors. The purpose of this study is to develop a new high-speed nanoprofiler that traces the normal vector of an aspheric mirror surface. The method of measurement adopted here is based upon the accuracy of a rotation goniometer. In order to attain a form measurement accuracy of PV1nm, it is necessary to improve the angle measurement accuracy. In this study, we equip a nanoprofiler with a rotary encoder that is calibrated in order to accomplish this objective, using a national standard machine. Consequently, this rotary encoder can be calibrated with an accuracy of ±0.12 μrad when considering the influence of installing the encoder on the nanoprofiler.

Katsuyosi Endo

Papers

Development of a High-Speed Nanoprofiler Using Normal Vector Tracing

Surface gradient integrated profiler for x-ray and EUV optics: self calibration method of measured position for an off-axis parabolic mirror (f=150mm) measurement

Absolute Calibration of the Rotary Encoder Considering the Influence on-Machine for Development of High-Speed Nanoprofiler