The flatness is one of the important geometric quantity such as a silicon wafer, a photo mask and ultra-precise optics for an extreme ultraviolet lithography, synchrotron radiation facilities and a gravitational wave interferometer. A Fizeau interferometer is in a high accurate flatness measurement equipment. In a Fizeau interferometer, the measurand is a gap distance between a reference flat and a specimen. The measurement accuracy of the Fizeau interferometer is limited by the flatness of the reference flat. The flatness of commercially reference flats is about λ/40 to λ/20 (15 nm - 30 nm). There is strong demand for developing that the flatness of reference flat is less than 10 nm. Thus, we developed a λ/100 (6.3 nm) reference flat which is attachable to a commercial Fizeau interferometer. The measurable diameter of the optical flat was φ100 mm. In the factory fields, the flatness of the reference flat mounted on a commercial Fizeau interferometer is required. We designed the reference flat using the finite element method (FEM) to decrease a deformation by mounting. The developed reference flat was evaluated by a scanning deflectometric profiler (SDP) and an ultra-high accurate Fizeau interferometer. Finally, the reference flat was validated through the evaluation results.
Absolute optical thickness is a fundamental parameter for the design of optical elements. In semiconductor industry,
it is necessary to measure the absolute optical thickness of the central part of the projection lenses with a high
accuracy. However, even when the geometrical thickness is perfectly known, a typical refractive index of fused-silica
has an ambiguity of 6 × 10<sup>-5</sup> that gives an uncertainty of 180 nm in the optical thickness for a 3 mm-thick plate.
Moreover, the optical thickness measured by white light interferometry and wavelength tuning interferometry is an
optical thickness with respect to not the ordinary refractive index but the group refractive index. We measured the
ordinary optical thickness of a fused silica plate of 6-inch square and 3 mm thickness by a wavelength tuning
interferometer with a tunable phase shifting technique. We assumed the typical refractive index and dispersion of
the fused silica as approximate values. The absolute interference order for the optical thickness was finally
estimated, which gives a measurement resolution of typically 10 nm for the optical thickness.
The surface flatness and the uniformity in thickness and refractive index of a mask-blank glass have been
requested in semiconductor industry. The absolute optical thickness of a mask-blank glass of seven-inch square
and 3mm thickness was measured by three-surface interferometry in a wavelength tuning Fizeau interferometer.
Wavelength-tuning interferometry can separate in frequency space the three interference signals of the surface
shape and the optical thickness. The wavelength of a tunable laser diode source was scanned linearly from 632
nm to 642 nm and a CCD detector recorded two thousand interference images. The number of phase variation of
the interference fringes during the wavelength scanning was counted by a temporal discrete Fourier transform.
The initial and final phases of the interferograms before and after the scanning were measured by a phase
shifting technique with fine tunings of the wavelengths at 632 nm and 642 nm. The optical thickness defined by
the group refractive index at the central wavelength of 337 nm can be measured by this technique. Experimental
results show that the cross talk in multiple-surface interferometry caused a systematic error of 2.0 microns in the
measured optical thickness.
Profiling of optical surfaces with discontinuous steps by monochromatic interferometry has the ambiguity of multiples of a quarter wavelength. Wavelength-tuning interferometry can measure these surfaces with a unit of synthetic wavelength that is usually much larger than that of the original source. In order to solve this problem, the fractional phases of the interferograms before and after wavelength tuning should be carefully estimated. Phase-shifting interferometry with a mechanical phase shift by a PZT transducer determines the fractional phases of the interferograms with a resolution of better than one part in 250 of the wavelength. After subtracting the mechanical drift of the test surface during wavelength tuning, the absolute distance between the test surface and the reference surface is measured with an uncertainty better than a quarter wavelength. An optical flat with two gauge blocks 1 mm in height contacting the surface is measured by a Fizeau interferometer. Experimental results demonstrate that the surface profile can finally be measured with an accuracy of 20 nm.
A phase-shifting interferometer (PSI) with equal phase steps, using a frequency-tunable diode laser and a Fabry-Perot cavity, is proposed for the Carre algorithm. The measurement accuracy of the Carre algorithm depends on the equality of the phase steps. Using the Fabry-Perot cavity as a highly stable optical frequency reference, a high degree of phase step equality can be realized in the PSI with an optical frequency shift. Our experimental scheme realizes an optical frequency step equality higher than 2.1×10<sup>-5</sup> and a measurement repeatability of λ/850.
An Rb-stabilized diode laser has been developed for use in a high-precision interferometer. The light source is a commercially available external-cavity tunable diode laser. The laser frequency is stabilized to a Doppler-free absorption line of Rb by the third-harmonic technique. The laser emits an output beam with a high power (more than 7 mW) and fast frequency modulation (10 kHz). The relative optical frequency uncertainty of 4.3×10–10 is achieved for a 0.01-s averaging time.
Two-dimensional holographic frequency-division demultiplexing using an acousto-optic modulator is proposed. In the proposed scheme, the image multiplexing side and the demultiplexed side are connected by one optical transmission facility. By using a parallel-aligned nematic liquid-crystal spatial light modulator (PAL-SLM) as a thin hologram, we successfully demonstrated image demultiplexing with carrier frequencies of approximately 80 MHz.
A simple rubidium stabilized diode laser has been developed for a gauge block interferometer. The laser light source is a commercially available external-cavity tunable diode laser (New Focus Inc.). Laser frequency stabilization is realized by the third-harmonic technique, where a fast frequency modulation (10 kHz) is applied on the current. The absolute laser frequency was calibrated by an absolute optical frequency measurement system using a femtosecond mode-locked laser. The relative uncertainty of the laser frequency reached 4.3×10<sup>-10</sup> for an averaging time of 0.01 s. The phase error in the interferometeric measurement due to the optical frequency modulation is theoretically indicated to be small enough to measure long gauge blocks of up to 1000 mm. Long gauge block measurement of up to 1000 mm was successfully demonstrated using the developed rubidium stabilized diode laser and the I<sub>2</sub>-stabilized offset locked He-Ne laser (633 nm).
We have developed a gauge block measurement system that uses three frequency-stabilized lasers. The stabilized lasers are as follows: an I<SUB>2</SUB> stabilized offset locked He-Ne laser, an I<SUB>2</SUB>-stabilized Nd:YAG laser, and a Rb-stabilized diode laser. The I<SUB>2</SUB>-stabilized offset locked He-Ne laser is commercially available and its relative wavelength uncertainty is 2.5 X 10<SUP>-11</SUP>. An I<SUB>2</SUB>-stabilized Nd:YAG laser and a Rb-stabilized diode laser was developed in our institute and their relative wavelength uncertainties are 5 X 10<SUP>-12</SUP> and 1 X 10<SUP>-9</SUP>, respectively. In the measurement system, laser beams were introduced to the interferometer using an optical multimode fiber. An interferometer fringe pattern was taken using a CCD camera and the excess fraction parts were calculated from the fringe pattern using the Fourier transform method. The excess fraction part obtained from the Rb-stabilized semiconductor laser was used only to determine the integer part of the fringe order, because the accuracy and stability of the wavelength were not sufficient for the long gauge block measurements. This interferometer can measure gauge blocks of up to 1000 nm long and the standard uncertainty of the interferometer is about 75 nm for a 1000 mm long gauge block.
We have established four I<SUB>2</SUB>-stabilized Nd:YAG lasers to verify the frequency reproducibility of the lasers. The observed square root Allan variance of the four lasers was between 1 to approximately 4 X 10<SUP>-14</SUP> depending on the obtained signal-to-noise ratio of the spectra, when the integration time is larger than 300 s. The observed frequency reproducibility of each laser was ranged from 9.1 X 10<SUP>-14</SUP> approximately 1.5 X 10<SUP>-13</SUP> (corresponding to frequency uncertainties of +/- 51 approximately 87 Hz). Frequency reproducibility of a group of lasers (four NRLM lasers) has been evaluated to be 8.2 X 10<SUP>-13</SUP> (corresponding to a frequency uncertainty of +/- 640 Hz). One of the four NRLM lasers is a compact I<SUB>2</SUB>- stabilized Nd:YAG laser which is suitable to be transported to other laboratories for international frequency comparisons. Using this portable laser, we have accomplished frequency comparisons of Nd:YAG lasers between several metrological institutes in different countries. The absolute optical frequencies of the NRLM lasers were determined with an uncertainty of about 1.5 kHz by the frequency comparison between the NRLM and the JILA (formerly the Joint Institute for Laboratory of Astrophysics), Boulder, CO.
A newly optically addressed spatial light modulator using a GaAs crystal plate has been developed for incoherent-to- coherent optical conversions of images. The device has the same structure as the Pockels readout optical modulator. The basic characteristics of the device were as follows: halfwave voltage, 10.5 kV; sensitivity, 0.65 (mu) J/cm<SUP>2</SUP> at visible light; resolution, 5.6 line pairs/mm. Its high frame rate operation (larger than 500 Hz) and high contrast ratio (larger than 700:1) were experimentally confirmed, and its applications to Fourier transform of images and joint transform correlations between images were also demonstrated.