The practical feature of Fresnel-lens has been traditionally designed to satisfy the phase-difference function for a certain object point which is the result of ultra-high index method. For many cases, the practical blazed surface is used only on one side of the lens. Thus, as shown by our former study, the aberration can be reproduced only for a certain object point and cannot be reproduced even in the vicinity of this certain object point. This means that the one side blazed Fresnel lens has intrinsically aberration whether it is basically designed by high-index method or not. Since DOE or Fresnel lens are applied to many optical lens, we should consider the aberration caused by one side blazed Fresnel lens especially for a precise optics. In this paper, we derive the limit of Fresnel lens as F -number of DOE or Fresnel lens surface.
We developed a craft kit of "Color Mixer" to understand easily the principle of reproducing colors while enjoying the craftwork with mixing colors using three LEDs. We will report on the composition of the kit and its outreach activity.
We have proposed the projection relations to restrain aberrations caused by change of object distance for some cases.
Now we comprehensively reconsider them for various cases. We theoretically develop the projection relations to
restrain coma aberration, sagittal and meridional field curvatures both for plane image and spherical image in two ways
of the view points of 3rd order aberration theory and direct method. We also confirm them by practical lens designing.
In order to produce various kind of circuit pattern in short-term cycle, mask-less exposure using DMD(digital mirror device)-mask is useful. Although not only fine resolution but also large DOF(depth of focus) can be obtained by using PSM(phase shifting mask), there exists forbidden pitch region for PSM. While the pattern pitch of PSM becomes fine, it cannot be resolved at a certain pitch and it will be resolved again at a finer pattern pitch. This un-resolvable region is called forbidden pitch region. It has been time consuming to predict this region by numerical calculation. Applying PSM to various fields, we should predict the region simply. In this paper, we derive analytical equations which give the optimal NA(Numerical Aperture) and finest resolution and also reveal forbidden region. In addition, we confirm the validity of analytical equation by numerical calculation using PROLITHTM. This result will be useful to apply PSM in practice.
An object distance range within which fine image can be obtained by focus adjustment is limited since aberrations are
caused by change of object distance. We have developed a novel optical design method to suppress variation of coma,
astigmatism and field curvature induced by change of object distance. Variation of astigmatism and field curvature can
be suppressed by introducing appropriate distortion. Also variation of coma caused by change of object distance can be
suppressed by using spherical image surface which pivot is located at the center of exit pupil.
Since CD has become extraordinary fine, the limited performance has been required for optics. Therefore
computational lithography like SMO has been applied. Then it is difficult to evaluate prospectively the fundamental
performance of future optical lithography. However prospective evaluation method might be useful to discuss the future
lithography. Thus we had already proposed the analytical equations to evaluate resolution of RETs with considering
depth of focus[1,2,4]. In this paper, we reconsider and revise the equations and evaluate the fundamental resolution of
immersion DPL(Double Patterning Lithography) and EUVL(Extreme Ultra Violet Lithography).
Even though odd-order aspherical surfaces have sometimes been used in optics, their meaning and effectiveness have not been discussed enough to be fully understood. However, we have already discussed and derived mathematically that odd-order aspherical surfaces cannot be represented in the form of a power series of even-order even when rotationally symmetric. We have also explained that this result does not contradict the fact that the set of Zernike's circle polynominals forms a complete system and that their rotational symmetric terms consist only of even-order terms of radial coordinates. First, we reconsider these mathematical discussions. Second, we reveal that the first- and third-order aspherical surfaces are valuable in practical lens designing for catoptoric projection optics of extreme ultraviolet lithography.
The conventional scalar imaging theories that are represented in the Fresnel-Kirchhoff diffraction formula or the Rayleigh-Sommerfeld diffraction formulae involve contradictions. By introducing incoming inclination factors not only for the diffraction surface but also for the image plane, we propose a new equation that fulfills both the self-consistency and the reciprocity theorem. We also confirm the validity of this new equation by both theoretical discussions and numerical calculations.
A phase-shifting interferometry (PSI) using a multi-longitudinal-mode blue laser diode was developed. Since the
longitudinal modes of a laser diode are located almost at even interval and changes synchronously with the injection
current, by setting an optical path difference between two arms of an interferometer in such a way that makes the
contrast of interferogram to be a maximum, the phase shift required for PSI can be obtained by changing the injection
current. Moreover, in such a condition, the PSI system works even mode hops occur. Theory and experimental results for
measuring the transmitted wavefront of an aspheric DVD pickup lens are presented.
Although wavefront aberration in stepper projection optics has been classified with respect to its spatial frequency on the pupil, the physical meaning of this classification has not been clarified. In this paper, we show that wavefront aberration can be classified into figure aberration, random aberration, and nonconserved aberration, by taking into consideration the theoretical effect of undulated wavefront aberration with respect to its spatial frequency. We also show that the predictions of this theoretical classification coincide with both the results of numerical simulations for random aberration and the experimentally measured values of local flare size. Since our classification has a clear physical meaning, it will be valuable and applicable in developing not only stepper projection optics but also other more general optics.
Recently, since micro optics have been widely used in many optical systems, it is desired to evaluate correctly the
performance of such a micro optics and design them properly. In order to estimate accurately the diffraction effect,
rigorous inclination factor of diffraction should be utilized.
In this paper, we derive theoretically the self-consistent inclination factor which satisfies the reciprocity theorem in
scalar imaging theory. By calculating numerically the point spread function in micro optics of no aberration, we also
confirm the self-consistency of this factor. That is, the point spread function calculated by the diffraction at a spherical
surface on the pupil coincides with that calculated by the diffraction at a plane on the same pupil.
Our result will be very useful for evaluating and designing micro optics.
A new type of a phase-shifting interferometer is presented, where two fringe patterns in quadrature are simultaneously formed on an image sensor plane using a 1/8 wave plate and a polarization prism. The quadrature phaseshifting fringe patterns are acquired in each state plane of the interferometer. The phase calculation method with these four fringes patterns gives two phase distributions which are phase sum and difference between two states of the interferometer. Two interferometric systems will be presented, one of which uses one illuminating light and mechanically moving parts of the interferometer, and the other utilizes two illuminating light with different wavelengths. We will present the principles of the methods and some experimental verifications will be also given.
An interferometric method for long distance position sensing is presented, which utilizes a polarization maintaining fiber a Faraday rotator. The measurement system, principles of phase cancellation and phase calculation of orthogonal arizations are described. Some experimental results are also given.
We have already revealed that wavefront aberration can be categorized into figure and random aberrations and also concluded that the phenomenon of local flare can be explained by the concept of random aberration [1]. In this report, considering the finer undulation of wavefront aberration, we introduce the new concept of non-conserved wavefront aberration. Considering these classified aberrations, we discuss the flare.
The effect of residual fine undulation on aspherical suface may not be always evaluated correctly. We make this problem clear both theoretically and numerically and proposed the simple and valuable equation for evaluating the fine undulation.
Real-time displacement and vibration measurements are presented, Which are based on a spatial phase-shifting with a tilt holographic interferogram. Three intensity data sampled at every one-third of the fringe spacing of the tilt fringes are used to calculate the phase and the modulation term of the fringe which are functions of a displacement and a vibration amplitude, respectively. Three-dimensional look-up tables perform the calculations in a TV repetition rate to give a phase distribution and a new fringe profile which contours the vibration amplitude. Experimental results are given in two cases of a displacement measurement for a cantilever-like object and a vibration measurement at resonant frequencies of a flat speaker.
A new method for measuring a wavelength and standing wave ratio of a surface acoustic wave(SAW) is presented, which is based on a heterodyne interferometer using first-order diffracted light beams from a SAW device and a grating. Phase and amplitude distributions of a beat signal from the interferometer by moving the substrate or the grating give such characteristics of the SAW. Experimental verifications are presented in two cases of the movements of the object and grating. Two-dimensional measurements around an interdigital transducer of a SAW device are also given.
Two real-time phase mapping methods for finge patterns are presented, which are based on a spatial phase-shifting with three fringe patterns, and on a spatial synchronous detection for a tilted fringe pattern. A digital TV-image processor is implemented which bases on the two fringe processing techniques. Applications of the present methods to surface shape measurements using a polarization interferometer and a fringe projection technique, and to a surface deformation measurement using a holographic interferometer are described. Worst phase errors are analyzed theoretically which are caused by an additive intensity noise of input fringe signals and a multiplicative intensity noise due to misalignments of a measuring system. A phase error due to a digitization of calculations is also evaluated numerically.
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