Takashi Gemma

Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry.

We propose a general approach to eliminating some error source effects in phase-calculation algorithms for phase-shifting interferometry. We express the actual phase shift in a convenient form that takes the errors into account and develop in series the detected phase from a generic algorithm. Setting to zero the terms of the series that involve unwanted errors leads to a set of linear equations for the algorithm coefficients, which can thus be found. By using this approach, one could develop an algorithm series for an individual interferometer based on relevant concerns about the main error sources in it and eliminate the error source effects to any desired order. Two examples of algorithm series, to eliminate distorted phase shifts caused by the geometric effect in an interferometer with a spherical Fizeau cavity and to eliminate vibration effects, are discussed.

Improved illumination system for spatial coherence control.

An improved illumination system is proposed for creating a temporally coherent and spatially incoherent extended source to be used for spatial coherence control and reconstruction of a coherent hologram. Taking into account the fact that a rotating ground glass does not behave as an ideal Lambertian diffuser, the new illumination system tailors the directivity of the scattered lights to direct the lights efficiently into an interferometer so that a spatial coherence function can be better controlled and detected with higher fidelity. Experimental results are presented that demonstrate improved performance of the proposed system.

Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL

In visible-light point diffraction interferometer (PDI), in order to achieve measurement error <0.1 - 0.2 nm rms, wavefront irregularity from the pinhole must be supressed as 0.05 - 0.1 nm rms in designing. It is so difficult to execute such high accurate (10-4λ) simulation because the numerical electromagnetic simulation shows slow convergence in the visible-region. We discussed this problem by using 2D-model and found simulation conditions to obtain significant results. By using the simulator, several kind of systematic erros have been analyzed and optimized.

Absolute accuracy evaluation of aspherical null testing for EUVL mirrors

Interferometric null metrology can produce highly precise figure of aspherical surfaces. However, because the measurement is a direct comparison of the tested surface with the reference wavefront of the null optics, measurement accuracy is equivalent to the quality of the reference null wavefront. Although the asymmetric aberration of the reference null wavefront can be calibrated by rotating the tested surface, it is more difficult to calibrate the rotationally symmetric errors. Especially, the aspherical surface of EUVL mirrors must to be measured with higher accuracy, 0.2~0.3nmRMS. We have developed an aspherical null testing system using a null lens for EUVL mirrors. We analyzed the uncertainty of null lens in each process and estimated the measurement accuracy of aspherical null testing using null lens. If the compensator lens contains only one piece of lens, the measurement accuracy is estimated to be 0.20nmRMS. If the compensator contains two pieces, the measurement accuracy becomes 0.24nmRMS. To verify our estimation, we evaluate a sample lens with aplanatic surfaces that make no spherical aberrations. In this case, we can evaluate the quality of the transmitted wavefront absolutely. The difference between the calculated and the experimental wavefronts is much smaller than our estimation. To this extent, our aspherical testing technique using null lens has been verified to be able to meet the high demanding for EUVL mirror testing.

testing at 1nm accuracy for sub-mm asphericity

This paper describes null interferometry at 1nm accuracy for testing aspherical surfaces of sub-mm deviation from the best fitting sphere. We have developed the two kinds of null compensators. The one is a “null lens” composed of almost perfect spherical surfaces and homogeneous glass. The other is a “zone plate” manufactured through the lithography process. The results of the two null testing were compared with the results by the ultra-precision CMM (Coordinate Measuring Machine). These totally different measurements differed only by an amount of 1.6nm rms. This result shows the accuracy of our null interferometry is almost 1nm rms.

Interferometry with Null Optics for Testing Aspherical Surfaces at 1nm Accuracy

This paper describes null interferometry at 1nm accuracy for testing aspherical surfaces of sub-mm deviation from the best fitting sphere. We have developed the two kinds of null compensators. The one was the null lens composed of almost “perfect” spherical surfaces and homogeneous glass. The other was the zone plate manufactured through the lithography process. The measurement results using these null compensators were compared with the results by the ultra-precision CMM (Coordinate Measuring Machine). These three measurements differed only by an amount of 1.6nm rms. This result proved the accuracy of our null interferometry was almost 1nm rms.