• Korean Journal of Optics and Photonics
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• v.11 no.4
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• pp.246-249
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• 2000

The null lens is designed for testing the elliptical (conic constant>O) mirror which is the third mirror of the off-axis Three Mirror Anastigmat (TMA) designed as a high resolution camera for remote sensing. The mixed type design is proposed as a new design type which has a small annular flat mirror, but has as twice sensitivity as the autostigmatic type design. It is also shown that the null lens of the Mixed type is better than that of the autostigmatic type in terms of the sensitivity of the wavefront distortion which is given as the magnitude of optical path difference with respect to the change of each surface parameters such as the radius of curvature, thickness of lenses and tested mirror.

• Korean Journal of Optics and Photonics
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• v.17 no.2
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• pp.186-190
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• 2006

The use of null optics is proposed as a new concept for the precise alignment of a confocal unstable resonator. The characteristics of the proposed null optics are investigated and analysed with the designed null lens for a real confocal unstable resonator of which the length is 3.5 m. As a result of the analysis, the pupil map data are shown about the despace error of 1.0 mm and tilt error of 1.0 mrad.

• Korean Journal of Optics and Photonics
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• v.17 no.5
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• pp.412-419
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• 2006

We design and fabricate an autostigmatic null lens system assembled in a fixed tube mount in order to evaluate the shape of an aluminum hyperbolic mirror with the diameter of 300 mm and the f-number of 1.98, which is fabricated by a high precision aspherical DTM (diamond turning machine). Also, we evaluate the degree of shape of the aspherical mirror by this autostigmatic null lens testing method. The autostigmatic null lens system assembling in a fixed tube mount has several advantages of light weight, good mechanical stability, etc. The permissible fabricating limits of null lenses and a mount are determined by considering various tolerances to assure the measurement reliability.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.869-877
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• 2022

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let M be a homology lens space with H₁(M; ℤ) ≅ ℤ_p and K a not null-homologous knot in M. We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H₁(L(p, q)).

• Korean Journal of Optics and Photonics
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• v.16 no.5
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• pp.440-445
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• 2005

The limitation of measurement accuracy and reliability of autostigmatic null lens system are studied for the cases of using inter-distance of null lenses as the adjustment factor of alignment and fixing the distance by mounting. If we investigate the first case, the wavefront aberration of null lens system is compensated by the adjustment process even though the shape of aspherical surface is not properly fabricated. As the result, it brings about the problem of measurement reliability. However, for the fixing process by mounting null lenses, it doesn't cause the reliability problem because the wavefront aberration of null lens system is not compensated. Further, the fixing process shows nearly same result in measurement accuracy to the adjustment process, that is, $0.0316{\lambda}$ vs. $0.0326{\lambda}$. So, we can conclude the setup for autostigmatic null lens system must be constituted by means of the fixing process. Meanwhile, we introduce and define the alignment aperture on aspheircal mirror, which can be approximated as spherical zone for alignment of null lens system, and besides, we calculate the required fabrication accuracy of the zone for the necessary measurement accuracy.

• Korean Journal of Optics and Photonics
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• v.12 no.5
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• pp.352-355
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• 2001

A null lens is designed for testing the hyperbolic mirror which is the first mirror of the off-axis three mirror anastigmat(TMA) designed as a high resolution camera for remote sensing. To choose a better null lens system for the hyperbolic surface under test, both autostigmatic and mixed type null lenses are designed and analysed for sensitivity with respect to change of each surface parameter such as the radius of curvature and the thickness.

• Proceedings of the Optical Society of Korea Conference
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• 2009.10a
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• pp.129-130
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• 2009

In order to determine the aberration coefficients of an aspheric lens with a small diameter, its transmitted wavefront was compensated with a null CGH and an auxiliary convex lens. The configuration of the measuring system and the fabrication step of CGHs could be simplified by using a reflective amplitude-type CGH as null optics. The compensated waterfronts of several sample lenses were measured and analyzed, and consequently the performance of the CGH was evaluated.

• Korean Journal of Optics and Photonics
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• v.16 no.1
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• pp.71-78
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• 2005

A null lens system of autostigmatic type, consisting of two mirrors, is designed for testing a large aspherical mirror. The system is theoretically analyzed to determine the limitation of measurement accuracy according to the manufacturing and alignment errors. We confirmed that irregularity of the null lens surface is the principal factor among tolerances in limiting measurement accuracy. Consequently, we can predict that measurement accuracy will be from 5λ/100 to 4λ/1000 according to the amount of this irregularity. That is, we can present the limitation of possible measurement accuracy with actual alignment and manufacturing errors.

• Korean Journal of Optics and Photonics
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• v.28 no.6
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• pp.281-289
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• 2017

In the present research, the optical measurement error induced by vibration of the optical measurement tower for large mirrors at KRISS (Korea Research Institute of Standards and Science) is investigated. The vibrations of the tower structure, the interferometer, and the null lens are measured while the surface errors of the 600-mm-diameter on-axis aspheric mirror are measuring, under various environmental conditions. The increase of surface error induced by alignment error with respect to vibration is analyzed. As a result, the interferometer and the null lens, which are located on the top of the tower, are highly sensitive to vibration. Additionally, the surface error of the mirror is strongly increased when the vibration directions of the interferometer and the null lens are different. To reduce the alignment error and the surface error induced by vibration, the tower structure should be improved, to be insensitive to low-frequency vibration. Alternatively, optical measuring under stable conditions by vibration monitoring can improve the reliability of the surface error measurement.

• Korean Journal of Optics and Photonics
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• v.17 no.2
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• pp.165-174
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• 2006

The autotstigmatic null lens system is designed and constructed for the fabrication of a parabolic mirror with the diameter of 450 mm(f/2.7). And the measurement reliability is also analyzed theoretically by means of the tolerancing technique using lens design software(CODE V). From this analysis, we can precisely fabricate a parabolic mirror with the large diameter of 450 mm(f/2.7). Meanwhile, in order to confirm the fabrication results by the autostigmatic method, the mirror surface is tested again by an autocollimating method that uses only a plane mirror without any null lens.